{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":52148,"title":"MATLAB Basics: Complex Argument","description":"For a given complex number, x, return the argument, y, in degrees.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 20px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 10px; transform-origin: 406.493px 10px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor a given complex number, x, return the argument, y, in degrees.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = argumentdeg(x)\r\n y = ;\r\nend","test_suite":"%%\r\nx = 1+i;\r\ny_correct = 45;\r\nassert(isequal(argumentdeg(x),y_correct))\r\n%%\r\nx = 45i;\r\ny_correct = 90;\r\nassert(isequal(argumentdeg(x),y_correct))\r\n%%\r\nx = 136;\r\ny_correct = 0;\r\nassert(isequal(argumentdeg(x),y_correct))\r\n%%\r\nx = 17-6i;\r\ny_correct = -(atan(6/17)*180/pi)\r\nassert(abs(argumentdeg(x)-y_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":1231855,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":69,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-28T14:26:52.000Z","updated_at":"2026-03-30T20:49:34.000Z","published_at":"2021-06-28T14:28:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given complex number, x, return the argument, y, in degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52133,"title":"MATLAB Basics: Complex Conjugates","description":"For a given complex number, x, return the complex conjugate, y.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 200.5px 8px; transform-origin: 200.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given complex number, x, return the complex conjugate, y.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = compconj(x)\r\n y = ;\r\nend","test_suite":"%%\r\nx = 1+i;\r\ny_correct = 1-i;\r\nassert(isequal(compconj(x),y_correct))\r\n%%\r\nx = 1-i;\r\ny_correct = 1+i;\r\nassert(isequal(compconj(x),y_correct))\r\n%%\r\nx = 3i;\r\ny_correct = -3i;\r\nassert(isequal(compconj(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = 7;\r\nassert(isequal(compconj(x),y_correct))\r\n%%\r\nx = 7-13i;\r\ny_correct = 7+13i;\r\nassert(isequal(compconj(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":1231855,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2021-06-28T19:38:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-28T14:07:04.000Z","updated_at":"2026-02-11T18:32:04.000Z","published_at":"2021-06-28T14:07:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given complex number, x, return the complex conjugate, y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52105,"title":"MATLAB Basics: Complex Numbers","description":"For a given complex number, x, return the real and imaginary parts as a vector, y = [Real Imaginary].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 20px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 10px; transform-origin: 406.493px 10px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor a given complex number, x, return the real and imaginary parts as a vector, y = [Real Imaginary].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = realimaginary(x)\r\n y = ;\r\nend","test_suite":"%%\r\nx = 1+i;\r\ny_correct = [1 1];\r\nassert(isequal(realimaginary(x),y_correct))\r\n%%\r\nx = 1.6+sqrt(2)*i;\r\ny_correct = [1.6 sqrt(2)];\r\nassert(isequal(realimaginary(x),y_correct))\r\n%%\r\nx = pi+156.78i;\r\ny_correct = [pi 156.78];\r\nassert(isequal(realimaginary(x),y_correct))\r\n%%\r\nx = 6i;\r\ny_correct = [0 6];\r\nassert(isequal(realimaginary(x),y_correct))\r\n%%\r\nx = 160000000;\r\ny_correct = [160000000 0];\r\nassert(isequal(realimaginary(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":1231855,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-25T08:23:44.000Z","updated_at":"2026-02-05T18:22:06.000Z","published_at":"2021-06-25T08:30:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given complex number, x, return the real and imaginary parts as a vector, y = [Real Imaginary].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1487,"title":"Sort complex numbers into complex conjugate pairs","description":"Sort complex numbers into complex conjugate pairs.\r\n\r\nExample: \r\n\r\n Input x = [3-6i -1-4i -1+4i 3+6i]\r\n\r\n Sorted output = [-1 - 4i -1 + 4i 3 - 6i 3 + 6i]","description_html":"\u003cp\u003eSort complex numbers into complex conjugate pairs.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input x = [3-6i -1-4i -1+4i 3+6i]\u003c/pre\u003e\u003cpre\u003e Sorted output = [-1 - 4i -1 + 4i 3 - 6i 3 + 6i]\u003c/pre\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx=[3-6i -1-4i -1+4i 3+6i];\r\ny_correct = [-1 - 4i -1 + 4i 3 - 6i 3 + 6i];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx=[2-i 2+i 3+4i 3-4i];\r\ny_correct = [2-i 2+i 3-4i 3+4i];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":1023,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":134,"test_suite_updated_at":"2013-05-02T00:26:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-02T00:22:41.000Z","updated_at":"2026-02-06T09:38:18.000Z","published_at":"2013-05-02T00:22:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSort complex numbers into complex conjugate pairs.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input x = [3-6i -1-4i -1+4i 3+6i]\\n\\n Sorted output = [-1 - 4i -1 + 4i 3 - 6i 3 + 6i]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2236,"title":"Complex transpose","description":"Calculate the transpose of a matrix having complex numbers as its elements without changing the signs of the imaginary part.\r\n\r\ne.g. a=[1+2i; 3-7i; 2i; 6]\r\n\r\n\r\nTranspose(a) = [1+2i, 3-7i, 2i, 6]\r\n\r\n","description_html":"\u003cp\u003eCalculate the transpose of a matrix having complex numbers as its elements without changing the signs of the imaginary part.\u003c/p\u003e\u003cp\u003ee.g. a=[1+2i; 3-7i; 2i; 6]\u003c/p\u003e\u003cp\u003eTranspose(a) = [1+2i, 3-7i, 2i, 6]\u003c/p\u003e","function_template":"function y = T(x)\r\n y = x';\r\nend","test_suite":"%%\r\nx =[1+2i; 3-7i; 2i; 6];\r\ny_correct = [1+2i, 3-7i, 2i, 6];\r\nassert(isequal(T(x),y_correct))\r\n\r\n%%\r\nx =[-2i -7i -2i -6i];\r\ny_correct =[-2i; -7i; -2i; -6i;];\r\nassert(isequal(T(x),y_correct))\r\n\r\n\r\n%%\r\nx =[1 2; 3 4;];\r\ny_correct =[1 3; 2 4;];\r\nassert(isequal(T(x),y_correct))\r\n\r\n%%\r\nx =[100+200i 3-4i 8-7.5i; 0.2+3i 0.005-0.23i -4];\r\ny_correct =[100+200i 0.2+3i; 3-4i 0.005-0.23i; 8-7.5i -4;];\r\nassert(isequal(T(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":16381,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":116,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-04T21:53:40.000Z","updated_at":"2026-02-06T20:54:56.000Z","published_at":"2014-03-04T21:54:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the transpose of a matrix having complex numbers as its elements without changing the signs of the imaginary part.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g. a=[1+2i; 3-7i; 2i; 6]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTranspose(a) = [1+2i, 3-7i, 2i, 6]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":53094,"title":"Easy Sequences 51: Positive Gaussian Primes","description":"A Gaussian Prime is a gaussian integer that cannot be decomposed as product of two non-unit gaussian integers (the complex units being: , , and ). We say that a gaussian prime , is positive, if and . \r\nWrite a function that counts the number of elements of set, ,of all positive gaussian primes , such that and are both .\r\nFor example, for , the complete set of positive gaussian primes are as follows: \r\n \r\nTherefore, for the function should return .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 226.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 113.25px; transform-origin: 407px 113.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Gaussian_integer#Gaussian_primes\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGaussian Prime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 316px 8px; transform-origin: 316px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a gaussian integer that cannot be decomposed as product of two non-unit gaussian integers (the complex units being: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAkCAYAAAD/yagrAAAAhUlEQVRYhe3XUQmAMBhF4ZPFAhYwgQlsYIM1sIsRDGMGK8wHBwoqCv5uE+8H99nDGMJARCS2MnXAlQYYgT51yJmaJdCHZRnaAW1Y1qFbCrWmUGsKtWYSWhksSqh/uClW6PBwdz7+rzsag0KtKdSSYw0dgSJtzl7DcoJHvzTHB95PIiLyshkwkls8t0LQOAAAAABJRU5ErkJggg==\" style=\"width: 21px; height: 18px;\" width=\"21\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAAkCAYAAAAD3IPhAAAAxElEQVRYhe2WUQ3DIBBAn4c6wEANoGAKcICDOsBCNUxCxVQDFroPYHQLfGxdel1yL7mEpgl5Oe4OQFGU/8YAo7QEgAW2HE7YhYkqswi7MGSJlYsclXJJDKmLHBBINRMkZTypaEsn3aRkCgtVZhB2IfLFfLE/iHdGalamT2S2gxEbe/rd/5Zsl+Vg3Dt79kRPp2SlJXoq+5vaC7u83NRG2OVZL2v+tsAsJVOyEkgtHhEcemXYrXkt+o5xpKOapUUURVEuwwPb9lEUVsiTiwAAAABJRU5ErkJggg==\" style=\"width: 17.5px; height: 18px;\" width=\"17.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102px 8px; transform-origin: 102px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). We say that a gaussian prime \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFEAAAAkCAYAAADxYNZEAAACaElEQVRoge2Y4ZGDIBBGXw90kAZswAqswA7SgR2khdSQEuwhLVhDWvB+4I6rh4gcnEmGN8NMJqgsH7vLAhQKhUKhUCh8OjVgzjbik+mBEXhShIxmVK0+2ZaPpQVewO1sQ0KQ1a7ONuSTKSIm4CtFNNhE2gJX9X8DdFNLmWj/S8QL1m7fOPXUOuABDBzcmS/TywPzxO7TRwfsVr/uS7H15xaxxdo9YOfXY53jMf3u1LMNdl5i0zN20Fp9RFbjovq1kCk8MpeIBivCyFIo1P8jVmSNnn/0znxluRJrb+tU/9q4GHKIWDELdXX0SyE98nt+ev7RTvLAPzEtYshKVcy5xtW0R/ieC0V74H3jGYmm3tGn5x+NfMA1ACxFXIeCC73qse11wP7bzjsX9V2Xl77wz38X7RmuAWApSkgI3qZ3tppOHVvPPALtrwLs106wtj9k/rvIKo4sNxPBsJx0ClLmRL2zujDMnjY4+n0CByO5ZMuVddJtYgdZkVLEvVDcy+cSGUfSxwLtZa5d1zAn5NDwCiGViDqUXQLp/q2dV9fAUTQ7A0ioHK7id0gloq++q7DepXOw733ZMHvcaW0TnU/WIrXkERDSiah33Sfz5GusgHJy2YokHeoGq8fhYlufRMQAw7zZpCisXaTMibrGk6Oe5G8dzq7SbH3IOJyy9Cr2WOE67Gq05L0eTymiwYohZdGV2faQykPO01HlTZKjTiRyM3Qo90TgO6UkIclR543RoZwrLf39qPPm6EjLcuWmt/Zsq3QycoiILqJ9GJa10zeKuHe19yfkJtvVcif5/6Bh+0Ij5PapUCh8Nz+BFDExDRXbcAAAAABJRU5ErkJggg==\" style=\"width: 40.5px; height: 18px;\" width=\"40.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 8px; transform-origin: 44.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is positive, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209px 8px; transform-origin: 209px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that counts the number of elements of set, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 31px; height: 20px;\" width=\"31\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eof all positive gaussian primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 40.5px; height: 18px;\" width=\"40.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 8px; transform-origin: 33.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e are both \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.5px 8px; transform-origin: 240.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the complete set of positive gaussian primes are as follows: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-26px\"\u003e\u003cimg src=\"data:image/png;base64,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style=\"width: 610px; height: 63.5px;\" width=\"610\" height=\"63.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85px 8px; transform-origin: 85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABXUlEQVRYhe1WXdHEIAxcD3VQAzWAgiqog3OAAyxUw0nAAxbQUAvfPZBMKcd/ezPfAzuTF9pNNyFsAQYGBv4HFgACwNzJi8Xemm8i0gHgzwtLCWv4IdcP3SrGUEIFQAJ4BwlLomRGTA3/Ag3XnSlYX3BWnauQu/Nq+WgKAq4bKewk6Mi886LnrTMXxVpIxFthMu9Yei7w3eXHwR1KbceG73kxtP64OJ4NnUluI4I4DjQOc0mMgZuvUqUCbutVQuB6V8iGq6dotA1syD/QuX184jTi7W8RxR1mvuwRFCKsNGcPMcyo87HupD2tr/GxZiicXVoauesvBIkbgphrfyGop0ru0P6kIHZj1cHlGbrlRSE0XMvD7ZqQv8jN6DhhPLCpi1iuQt8SJK4nkH3IoHHu+IO+K0sK/nWkEoYGaomnSGzsjlXEBPcn114oWqtx5g2nu/NFT1ZyBwYGBgZCfADd+JnFh3N7+AAAAABJRU5ErkJggg==\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = countSGPP(n)\r\n c = n;\r\nend","test_suite":"%%\r\nn = 10;\r\nc_correct = 35;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nns = 20:1:50;\r\ncs = arrayfun(@(n) countSGPP(n),ns);\r\nss = floor([mean(cs) median(cs) mode(cs) std(cs)]);\r\nss_correct = [261 255 103 109];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 100;\r\nc_correct = 1536;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nns = 200:10:500;\r\ncs = arrayfun(@(n) countSGPP(n),ns);\r\nss = floor([mean(cs) median(cs) mode(cs) std(cs)]);\r\nss_correct = [15076 14363 5253 6783];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 1234;\r\nc_correct = 144547;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nn = 5678;\r\nc_correct = 2490874;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nns = 400:400:10000;\r\ncs = arrayfun(@(n) countSGPP(n),ns);\r\nss = floor([mean(cs) median(cs) mode(cs) std(cs)]);\r\nss_correct = [2655106 2112268 18293 2278026];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 12345;\r\nc_correct = 10756553;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nfiletext = fileread('countSGPP.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-20T16:50:27.000Z","updated_at":"2026-03-19T11:03:41.000Z","published_at":"2021-11-23T10:00:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Gaussian_integer#Gaussian_primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGaussian Prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a gaussian integer that cannot be decomposed as product of two non-unit gaussian integers (the complex units being: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). We say that a gaussian prime \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep+qi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is positive, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\\\\ge0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that counts the number of elements of set, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{GP+}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eof all positive gaussian primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep+qi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e are both \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the complete set of positive gaussian primes are as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{GP+} = \\\\{\\\\ 3,\\\\ 7,\\\\ 1+i,\\\\ 1+2i,\\\\ 1+4i,\\\\ 1+6i,\\\\ 1+10i,\\\\ 2+i,\\\\ 2+3i,\\\\ 2+5i,\\\\ 2+7i,\\\\ 3+2i,\\\\ 3+8i,\\\\\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ 3+10i\\\\ 4+i,\\\\ 4+5i,\\\\ 4+9i,\\\\ 5+2i,\\\\ 5+4i,\\\\ 5+6i,\\\\ 5+8i,\\\\ 6+i,\\\\ 6+5i,\\\\ 7+2i,\\\\ 7+8i,\\\\\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ 7+10i,\\\\ 8+3i,\\\\ 8+5i,\\\\ 8+7i,\\\\ 9+4i,\\\\ 9+10i,\\\\ 10+i,\\\\ 10+3i,\\\\ 10+7i, 10+9i\\\\ \\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e35\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46025,"title":"Evaluate the gamma function","description":"The gamma function is a generalization of the factorial, and it appears in many applications such as evaluating certain integrals, working with probability distributions, and evaluating fractional derivatives. MATLAB includes the function gamma, but it accepts only real arguments.\r\nWrite a function that evaluates the gamma function for complex arguments.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93.3333px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 46.6667px; transform-origin: 407.5px 46.6667px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.6667px; text-align: left; transform-origin: 384.5px 31.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.0583px 7.66667px; transform-origin: 12.0583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.66667px; transform-origin: 1.94167px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/GammaFunction.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003egamma function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.642px 7.66667px; transform-origin: 302.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a generalization of the factorial, and it appears in many applications such as evaluating certain integrals, working with probability distributions, and evaluating fractional derivatives. MATLAB includes the function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.66667px; transform-origin: 1.94167px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 7.66667px; transform-origin: 19.25px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; \"\u003egamma\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.66667px; transform-origin: 3.88333px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but it accepts only real arguments.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 232.467px 7.66667px; transform-origin: 232.467px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that evaluates the gamma function for complex arguments.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = gamma2(z)\r\n y = f(z);\r\nend","test_suite":"%%\r\nz = 3+2i;\r\ny = gamma2(z);\r\ny_correct = -0.4226372863112003 + 0.871814255696503i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = 1+i;\r\ny = gamma2(z);\r\ny_correct = 0.4980156681183556 -0.1549498283018104i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = (1+i)/2;\r\ny = gamma2(z);\r\ny_correct = 0.818163995 - 0.7633138287i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = i;\r\ny = gamma2(z);\r\ny_correct = -0.154949828301810 - 0.4980156681183566i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = 5i;\r\ny = gamma2(z);\r\ny_correct = -0.00027170388350615125 + 0.0003399328988721375i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = 1/2 + 14.1i;\r\ny = gamma2(z);\r\ny_correct = -2.0555298837259187e-10 - 5.667644214210669e-10i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = -1+i;\r\ny = gamma2(z);\r\ny_correct = -0.1715329199082727 + 0.3264827482100833i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = -2-3i;\r\ny = gamma2(z);\r\ny_correct = -0.0001631724182726072 - 0.001128495917017955i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = 10*(rand+0.02);\r\ny_correct = gamma(z);\r\nassert(abs(gamma2(z)-y_correct)/y_correct \u003c 1e-6)\r\n\r\n%%\r\nfiletext = fileread('gamma2.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'system'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":9,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2022-01-30T20:31:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-04T16:14:47.000Z","updated_at":"2026-01-09T11:39:54.000Z","published_at":"2020-07-05T04:43:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/GammaFunction.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003egamma function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a generalization of the factorial, and it appears in many applications such as evaluating certain integrals, working with probability distributions, and evaluating fractional derivatives. MATLAB includes the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egamma\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, but it accepts only real arguments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that evaluates the gamma function for complex arguments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53079,"title":"Easy Sequences 50: Blocked Gaussian Integers","description":"A Gaussian Integer is a complex number whose real and imaginary parts are both integers.\r\nA gaussian integer is said to be blocked with respect to another gaussian integer , if the line segment connecting and on the complex plane, pass through at least one more gaussian integer. In the figure below, where , the red colored points represents the blocked gaussian integers with respect to , While the green points represents unblocked gaussian integers.\r\n \r\nIn the above figure, blocked gaussian points, , and , are shown. These points lie within the a square with side lengths , in which is at the center. But these are not the only blocked gaussian points for this case. and are also blocked points. The sum total of all blocked gaussian integers relative to and bounded by the square with side and is .\r\nGiven a gaussian integer , centered at a square of side , find the absolute value of the sum of all blocked gaussian integers around , with respect to , that lies within the square (including, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: .\r\nPlease round-off your answer to 4 decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 722.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 361.25px; transform-origin: 407px 361.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Gaussian_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGaussian Integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 225px 8px; transform-origin: 225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a complex number whose real and imaginary parts are both integers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61px 8px; transform-origin: 61px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA gaussian integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAkCAYAAABixKGjAAAA00lEQVRIie2VQQ3DMAxFH4cwGIESKIIhCIMyKINRKIZBKIdQGIZSaA+2parKdkgcaarypKi3b+f7u4FO51YEYNavOxHYgbGF+BtYadB5QLp+egujok26Blho5HURA+Ljr7OUik8q8EH8PJ8NSBWNs2qBK1ELVg0vJzwgXQ81wjmCCjfJciJ/m2oWZL3dmahMxjdGHJKRw5Lx8BYOiBXRWxhkeLbiK44/pRdix3YqcF2cRKFlZxFb9V0FbbBWuPpG9vBuiF2WINfcB+QmM//0MHRuxAHmODh6hQd5nwAAAABJRU5ErkJggg==\" style=\"width: 11.5px; height: 18px;\" width=\"11.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42px 8px; transform-origin: 42px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is said to be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eblocked\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.5px 8px; transform-origin: 130.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with respect to another gaussian integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, if the line segment connecting \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAkCAYAAABixKGjAAAA00lEQVRIie2VQQ3DMAxFH4cwGIESKIIhCIMyKINRKIZBKIdQGIZSaA+2parKdkgcaarypKi3b+f7u4FO51YEYNavOxHYgbGF+BtYadB5QLp+egujok26Blho5HURA+Ljr7OUik8q8EH8PJ8NSBWNs2qBK1ELVg0vJzwgXQ81wjmCCjfJciJ/m2oWZL3dmahMxjdGHJKRw5Lx8BYOiBXRWxhkeLbiK44/pRdix3YqcF2cRKFlZxFb9V0FbbBWuPpG9vBuiF2WINfcB+QmM//0MHRuxAHmODh6hQd5nwAAAABJRU5ErkJggg==\" style=\"width: 11.5px; height: 18px;\" width=\"11.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.5px 8px; transform-origin: 311.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on the complex plane, pass through at least one more gaussian integer. In the figure below, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 63.5px; height: 18px;\" width=\"63.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the red colored points represents the blocked gaussian integers with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113px 8px; transform-origin: 113px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, While the green points represents unblocked gaussian integers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 404.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 202.25px; text-align: left; transform-origin: 384px 202.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the above figure, blocked gaussian points, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAkCAYAAAB15jFqAAABMUlEQVRYhe2WUZHDMAxEHwczKIEQCIIgCIMwKIOjEAyGEA6hYAylcPdha0buJbac5uvOO6Of1NYqWWlV6Oj46xhTDBfvOuthB6zA91u8gMWYY0t3dgvxIyV/J9TxZSDV50dLhQGY1bOB328+VfLMqfhqgVM6eKbfU5H6WjIrPGXNHLm+t2AlalqCNMhtpBYI6Xbwm4zXk/jVAg0jU0JIpEcyTOQNt99B+EjJAucyjLSNVhXSvaVmW2iYzxocsXmOtNTwivRjeGyWJm5WK66KhahjzfS1nlaPPsRsJITcsa5spWZCuME4JgPhQD468pbrFcKBWG2p5R2xsYRU6ykbaqNuqxnhTtToLAJ5h2o95U+AyRyEsLTAz3aqNoWdhtXnU/WW8OQz69T9j8alo6PjH+IHu6B/3OiYY/8AAAAASUVORK5CYII=\" style=\"width: 14.5px; height: 18px;\" width=\"14.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39px; height: 18px;\" width=\"39\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39px; height: 18px;\" width=\"39\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168px 8px; transform-origin: 168px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, are shown. These points lie within the a square with side lengths \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31px 8px; transform-origin: 31px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in which \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 63.5px; height: 18px;\" width=\"63.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.5px 8px; transform-origin: 256.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is at the center. But these are not the only blocked gaussian points for this case. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 49.5px; height: 18px;\" width=\"49.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39px; height: 18px;\" width=\"39\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.5px 8px; transform-origin: 258.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are also blocked points. The sum total of all blocked gaussian integers relative to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 63.5px; height: 18px;\" width=\"63.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and bounded by the square with side \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 54px; height: 18px;\" width=\"54\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90px 8px; transform-origin: 90px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a gaussian integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, centered at a square of side \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33px 8px; transform-origin: 33px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eabsolute value of the sum\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51px 8px; transform-origin: 51px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e of all blocked gaussian integers around \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.5px 8px; transform-origin: 56.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95px 8px; transform-origin: 95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that lies within the square\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eincluding\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 153px; height: 18.5px;\" width=\"153\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease round-off your answer to 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function absSum = blockedGaussian(z,a)\r\n z = a;\r\nend","test_suite":"%%\r\nz = 3+2i; a = 9;\r\nabsSum_correct = 115.3776;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = 7-10i; a = 99;\r\nabsSum_correct = 45994.3016;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = -1-i; a = 999;\r\nabsSum_correct = 552493.6408;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = -4+5i; a = 9999;\r\nabsSum_correct = 250953396.5632;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = 10+i; a = 99999;\r\nabsSum_correct = 39401199538.8094;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = [1+2i 3-2i 7+7i]; a = 123456;\r\nabsSum_correct = [13362525603.2731 21546425116.3652 59158422678.1219];\r\nabsSum = blockedGaussian(z,a)\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = arrayfun(@(x) x + i*(x-1)*(-1)^x,1:100); a = 7777;\r\nstat_correct = [1677439212.6962 1677263085.6360 23718896.0000 972842722.3354];\r\nabsSum = blockedGaussian(z,a);\r\nstat = round([mean(absSum) median(absSum) mode(absSum) std(absSum)],4);\r\nassert(isequal(stat,stat_correct))\r\n%%\r\nz = -123+456i; a = 2:2:2000;\r\nstat_correct = [247640834.4715 185966225.8317 0.0000 221359619.596];\r\nabsSum = arrayfun(@(b) blockedGaussian(z,b),a);\r\nstat = round([mean(absSum) median(absSum) mode(absSum) std(absSum)],4)\r\nassert(isequal(stat,stat_correct))\r\n%%\r\nfiletext = fileread('blockedGaussian.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2021-11-18T04:24:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-16T06:04:44.000Z","updated_at":"2025-10-07T14:22:21.000Z","published_at":"2021-11-17T07:50:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Gaussian_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGaussian Integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a complex number whose real and imaginary parts are both integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA gaussian integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is said to be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eblocked\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with respect to another gaussian integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, if the line segment connecting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e on the complex plane, pass through at least one more gaussian integer. In the figure below, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=3+2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the red colored points represents the blocked gaussian integers with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, While the green points represents unblocked gaussian integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the above figure, blocked gaussian points, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7+6i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, are shown. These points lie within the a square with side lengths \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, in which \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=3+2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is at the center. But these are not the only blocked gaussian points for this case. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-1-2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7+2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are also blocked points. The sum total of all blocked gaussian integers relative to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=3+2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and bounded by the square with side \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e96+64i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a gaussian integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, centered at a square of side \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eabsolute value of the sum\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e of all blocked gaussian integers around \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that lies within the square\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eincluding\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|\\\\ 96+64i\\\\ |=115.3776\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease round-off your answer to 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpeg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpeg\",\"contentType\":\"image/jpeg\",\"content\":\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAMxNAAAkpIAAgAAAAMxNAAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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Basics: Complex Argument","description":"For a given complex number, x, return the argument, y, in degrees.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 20px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 10px; transform-origin: 406.493px 10px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor a given complex number, x, return the argument, y, in degrees.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = argumentdeg(x)\r\n y = ;\r\nend","test_suite":"%%\r\nx = 1+i;\r\ny_correct = 45;\r\nassert(isequal(argumentdeg(x),y_correct))\r\n%%\r\nx = 45i;\r\ny_correct = 90;\r\nassert(isequal(argumentdeg(x),y_correct))\r\n%%\r\nx = 136;\r\ny_correct = 0;\r\nassert(isequal(argumentdeg(x),y_correct))\r\n%%\r\nx = 17-6i;\r\ny_correct = -(atan(6/17)*180/pi)\r\nassert(abs(argumentdeg(x)-y_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":1231855,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":69,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-28T14:26:52.000Z","updated_at":"2026-03-30T20:49:34.000Z","published_at":"2021-06-28T14:28:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given complex number, x, return the argument, y, in degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52133,"title":"MATLAB Basics: Complex Conjugates","description":"For a given complex number, x, return the complex conjugate, y.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 200.5px 8px; transform-origin: 200.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given complex number, x, return the complex conjugate, y.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = compconj(x)\r\n y = ;\r\nend","test_suite":"%%\r\nx = 1+i;\r\ny_correct = 1-i;\r\nassert(isequal(compconj(x),y_correct))\r\n%%\r\nx = 1-i;\r\ny_correct = 1+i;\r\nassert(isequal(compconj(x),y_correct))\r\n%%\r\nx = 3i;\r\ny_correct = -3i;\r\nassert(isequal(compconj(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = 7;\r\nassert(isequal(compconj(x),y_correct))\r\n%%\r\nx = 7-13i;\r\ny_correct = 7+13i;\r\nassert(isequal(compconj(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":1231855,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2021-06-28T19:38:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-28T14:07:04.000Z","updated_at":"2026-02-11T18:32:04.000Z","published_at":"2021-06-28T14:07:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given complex number, x, return the complex conjugate, y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52105,"title":"MATLAB Basics: Complex Numbers","description":"For a given complex number, x, return the real and imaginary parts as a vector, y = [Real Imaginary].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 20px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 10px; transform-origin: 406.493px 10px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10px; text-align: left; transform-origin: 383.498px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor a given complex number, x, return the real and imaginary parts as a vector, y = [Real Imaginary].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = realimaginary(x)\r\n y = ;\r\nend","test_suite":"%%\r\nx = 1+i;\r\ny_correct = [1 1];\r\nassert(isequal(realimaginary(x),y_correct))\r\n%%\r\nx = 1.6+sqrt(2)*i;\r\ny_correct = [1.6 sqrt(2)];\r\nassert(isequal(realimaginary(x),y_correct))\r\n%%\r\nx = pi+156.78i;\r\ny_correct = [pi 156.78];\r\nassert(isequal(realimaginary(x),y_correct))\r\n%%\r\nx = 6i;\r\ny_correct = [0 6];\r\nassert(isequal(realimaginary(x),y_correct))\r\n%%\r\nx = 160000000;\r\ny_correct = [160000000 0];\r\nassert(isequal(realimaginary(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":1231855,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-25T08:23:44.000Z","updated_at":"2026-02-05T18:22:06.000Z","published_at":"2021-06-25T08:30:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given complex number, x, return the real and imaginary parts as a vector, y = [Real Imaginary].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1487,"title":"Sort complex numbers into complex conjugate pairs","description":"Sort complex numbers into complex conjugate pairs.\r\n\r\nExample: \r\n\r\n Input x = [3-6i -1-4i -1+4i 3+6i]\r\n\r\n Sorted output = [-1 - 4i -1 + 4i 3 - 6i 3 + 6i]","description_html":"\u003cp\u003eSort complex numbers into complex conjugate pairs.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input x = [3-6i -1-4i -1+4i 3+6i]\u003c/pre\u003e\u003cpre\u003e Sorted output = [-1 - 4i -1 + 4i 3 - 6i 3 + 6i]\u003c/pre\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx=[3-6i -1-4i -1+4i 3+6i];\r\ny_correct = [-1 - 4i -1 + 4i 3 - 6i 3 + 6i];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx=[2-i 2+i 3+4i 3-4i];\r\ny_correct = [2-i 2+i 3-4i 3+4i];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":1023,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":134,"test_suite_updated_at":"2013-05-02T00:26:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-02T00:22:41.000Z","updated_at":"2026-02-06T09:38:18.000Z","published_at":"2013-05-02T00:22:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSort complex numbers into complex conjugate pairs.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input x = [3-6i -1-4i -1+4i 3+6i]\\n\\n Sorted output = [-1 - 4i -1 + 4i 3 - 6i 3 + 6i]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2236,"title":"Complex transpose","description":"Calculate the transpose of a matrix having complex numbers as its elements without changing the signs of the imaginary part.\r\n\r\ne.g. a=[1+2i; 3-7i; 2i; 6]\r\n\r\n\r\nTranspose(a) = [1+2i, 3-7i, 2i, 6]\r\n\r\n","description_html":"\u003cp\u003eCalculate the transpose of a matrix having complex numbers as its elements without changing the signs of the imaginary part.\u003c/p\u003e\u003cp\u003ee.g. a=[1+2i; 3-7i; 2i; 6]\u003c/p\u003e\u003cp\u003eTranspose(a) = [1+2i, 3-7i, 2i, 6]\u003c/p\u003e","function_template":"function y = T(x)\r\n y = x';\r\nend","test_suite":"%%\r\nx =[1+2i; 3-7i; 2i; 6];\r\ny_correct = [1+2i, 3-7i, 2i, 6];\r\nassert(isequal(T(x),y_correct))\r\n\r\n%%\r\nx =[-2i -7i -2i -6i];\r\ny_correct =[-2i; -7i; -2i; -6i;];\r\nassert(isequal(T(x),y_correct))\r\n\r\n\r\n%%\r\nx =[1 2; 3 4;];\r\ny_correct =[1 3; 2 4;];\r\nassert(isequal(T(x),y_correct))\r\n\r\n%%\r\nx =[100+200i 3-4i 8-7.5i; 0.2+3i 0.005-0.23i -4];\r\ny_correct =[100+200i 0.2+3i; 3-4i 0.005-0.23i; 8-7.5i -4;];\r\nassert(isequal(T(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":16381,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":116,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-04T21:53:40.000Z","updated_at":"2026-02-06T20:54:56.000Z","published_at":"2014-03-04T21:54:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the transpose of a matrix having complex numbers as its elements without changing the signs of the imaginary part.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g. a=[1+2i; 3-7i; 2i; 6]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTranspose(a) = [1+2i, 3-7i, 2i, 6]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":53094,"title":"Easy Sequences 51: Positive Gaussian Primes","description":"A Gaussian Prime is a gaussian integer that cannot be decomposed as product of two non-unit gaussian integers (the complex units being: , , and ). We say that a gaussian prime , is positive, if and . \r\nWrite a function that counts the number of elements of set, ,of all positive gaussian primes , such that and are both .\r\nFor example, for , the complete set of positive gaussian primes are as follows: \r\n \r\nTherefore, for the function should return .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 226.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 113.25px; transform-origin: 407px 113.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Gaussian_integer#Gaussian_primes\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGaussian Prime\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; 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height: 18px;\" width=\"21\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAAkCAYAAAAD3IPhAAAAxElEQVRYhe2WUQ3DIBBAn4c6wEANoGAKcICDOsBCNUxCxVQDFroPYHQLfGxdel1yL7mEpgl5Oe4OQFGU/8YAo7QEgAW2HE7YhYkqswi7MGSJlYsclXJJDKmLHBBINRMkZTypaEsn3aRkCgtVZhB2IfLFfLE/iHdGalamT2S2gxEbe/rd/5Zsl+Vg3Dt79kRPp2SlJXoq+5vaC7u83NRG2OVZL2v+tsAsJVOyEkgtHhEcemXYrXkt+o5xpKOapUUURVEuwwPb9lEUVsiTiwAAAABJRU5ErkJggg==\" style=\"width: 17.5px; height: 18px;\" width=\"17.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102px 8px; transform-origin: 102px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). We say that a gaussian prime \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 40.5px; height: 18px;\" width=\"40.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 8px; transform-origin: 44.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is positive, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209px 8px; transform-origin: 209px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that counts the number of elements of set, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 31px; height: 20px;\" width=\"31\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eof all positive gaussian primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 40.5px; height: 18px;\" width=\"40.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 8px; transform-origin: 33.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e are both \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.5px 8px; transform-origin: 240.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the complete set of positive gaussian primes are as follows: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-26px\"\u003e\u003cimg 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style=\"width: 610px; height: 63.5px;\" width=\"610\" height=\"63.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAkCAYAAAANdf2OAAACA0lEQVRoge2YXZWDMBBGr4c4wAAGqqAKcFAHOKiFakACHrBQDVjYfWjmMLDZMCndU+jOPScvZPLDl8lkEnAcx3Ecx3HKCUD1RJtTLOHlM/oQAtACI3AxtjkBPTDEttfY/kr5In00IuxXLBaBm2jbM/faOn4fcZGpeHhbA9ywC1wr2zpR38a64WUz/QBO2AXuyQtYFfT1b7AKrL33mrG74148wyrwVdk1GbtO2RXH4sDP2FPFSR41sFsF7snHX6HFthAAnGODnum0lUlUi0HHlYGX6BxyS9m6sFaBdbZhFTgXSoDJOyWuiNvXccC2tEOF/rEtZethYhVYj2kVuLNOYmDK/Srm3qonuLolFHXsb2s5F4yZolTgsaA/k8BhMYGBuZAXVX/E6+IzAuf+80yhwLpBzyMx19xU3RF5e4jQN517ol6Cf2vpbIf8ZRZhOh/0AbeMd2tXxxxHyyK0o1kFXj0ftIApd5f4uxb4Uxwti2iMduLppkcffYClVkM6W8ZlC0fLIgJTOMz9r9iY4q9ejdSAy/SsozxUvJuSxx7Z/r9lEjohMOkgxqkV01smRJuSi8ZeKBEYpjtBylYc0nTg69VIbUMdPgYKbi07IjB/nOlYz+UDk8iN+iaHoNnJGqY4l5tcT9kNbi/IG8uydLFuTWh5rJd2LccLj47jOI7jOI7jHJ1vW/g1szUietQAAAAASUVORK5CYII=\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85px 8px; transform-origin: 85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the function should return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = countSGPP(n)\r\n c = n;\r\nend","test_suite":"%%\r\nn = 10;\r\nc_correct = 35;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nns = 20:1:50;\r\ncs = arrayfun(@(n) countSGPP(n),ns);\r\nss = floor([mean(cs) median(cs) mode(cs) std(cs)]);\r\nss_correct = [261 255 103 109];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 100;\r\nc_correct = 1536;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nns = 200:10:500;\r\ncs = arrayfun(@(n) countSGPP(n),ns);\r\nss = floor([mean(cs) median(cs) mode(cs) std(cs)]);\r\nss_correct = [15076 14363 5253 6783];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 1234;\r\nc_correct = 144547;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nn = 5678;\r\nc_correct = 2490874;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nns = 400:400:10000;\r\ncs = arrayfun(@(n) countSGPP(n),ns);\r\nss = floor([mean(cs) median(cs) mode(cs) std(cs)]);\r\nss_correct = [2655106 2112268 18293 2278026];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nn = 12345;\r\nc_correct = 10756553;\r\nassert(isequal(countSGPP(n),c_correct))\r\n%%\r\nfiletext = fileread('countSGPP.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-20T16:50:27.000Z","updated_at":"2026-03-19T11:03:41.000Z","published_at":"2021-11-23T10:00:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Gaussian_integer#Gaussian_primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGaussian Prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a gaussian integer that cannot be decomposed as product of two non-unit gaussian integers (the complex units being: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). We say that a gaussian prime \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep+qi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is positive, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\\\\ge0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that counts the number of elements of set, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{GP+}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eof all positive gaussian primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep+qi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e are both \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the complete set of positive gaussian primes are as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_{GP+} = \\\\{\\\\ 3,\\\\ 7,\\\\ 1+i,\\\\ 1+2i,\\\\ 1+4i,\\\\ 1+6i,\\\\ 1+10i,\\\\ 2+i,\\\\ 2+3i,\\\\ 2+5i,\\\\ 2+7i,\\\\ 3+2i,\\\\ 3+8i,\\\\\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ 3+10i\\\\ 4+i,\\\\ 4+5i,\\\\ 4+9i,\\\\ 5+2i,\\\\ 5+4i,\\\\ 5+6i,\\\\ 5+8i,\\\\ 6+i,\\\\ 6+5i,\\\\ 7+2i,\\\\ 7+8i,\\\\\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ 7+10i,\\\\ 8+3i,\\\\ 8+5i,\\\\ 8+7i,\\\\ 9+4i,\\\\ 9+10i,\\\\ 10+i,\\\\ 10+3i,\\\\ 10+7i, 10+9i\\\\ \\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the function should return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e35\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46025,"title":"Evaluate the gamma function","description":"The gamma function is a generalization of the factorial, and it appears in many applications such as evaluating certain integrals, working with probability distributions, and evaluating fractional derivatives. MATLAB includes the function gamma, but it accepts only real arguments.\r\nWrite a function that evaluates the gamma function for complex arguments.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93.3333px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 46.6667px; transform-origin: 407.5px 46.6667px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.6667px; text-align: left; transform-origin: 384.5px 31.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.0583px 7.66667px; transform-origin: 12.0583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.66667px; transform-origin: 1.94167px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/GammaFunction.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003egamma function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.642px 7.66667px; transform-origin: 302.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a generalization of the factorial, and it appears in many applications such as evaluating certain integrals, working with probability distributions, and evaluating fractional derivatives. MATLAB includes the function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.66667px; transform-origin: 1.94167px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 7.66667px; transform-origin: 19.25px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; \"\u003egamma\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.66667px; transform-origin: 3.88333px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but it accepts only real arguments.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 232.467px 7.66667px; transform-origin: 232.467px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that evaluates the gamma function for complex arguments.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = gamma2(z)\r\n y = f(z);\r\nend","test_suite":"%%\r\nz = 3+2i;\r\ny = gamma2(z);\r\ny_correct = -0.4226372863112003 + 0.871814255696503i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = 1+i;\r\ny = gamma2(z);\r\ny_correct = 0.4980156681183556 -0.1549498283018104i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = (1+i)/2;\r\ny = gamma2(z);\r\ny_correct = 0.818163995 - 0.7633138287i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = i;\r\ny = gamma2(z);\r\ny_correct = -0.154949828301810 - 0.4980156681183566i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = 5i;\r\ny = gamma2(z);\r\ny_correct = -0.00027170388350615125 + 0.0003399328988721375i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = 1/2 + 14.1i;\r\ny = gamma2(z);\r\ny_correct = -2.0555298837259187e-10 - 5.667644214210669e-10i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = -1+i;\r\ny = gamma2(z);\r\ny_correct = -0.1715329199082727 + 0.3264827482100833i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = -2-3i;\r\ny = gamma2(z);\r\ny_correct = -0.0001631724182726072 - 0.001128495917017955i;\r\nassert(abs((real(y)-real(y_correct))/real(y_correct)) \u003c 1e-6)\r\nassert(abs((imag(y)-imag(y_correct))/imag(y_correct)) \u003c 1e-6)\r\n\r\n%%\r\nz = 10*(rand+0.02);\r\ny_correct = gamma(z);\r\nassert(abs(gamma2(z)-y_correct)/y_correct \u003c 1e-6)\r\n\r\n%%\r\nfiletext = fileread('gamma2.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'system'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":9,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2022-01-30T20:31:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-04T16:14:47.000Z","updated_at":"2026-01-09T11:39:54.000Z","published_at":"2020-07-05T04:43:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/GammaFunction.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003egamma function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a generalization of the factorial, and it appears in many applications such as evaluating certain integrals, working with probability distributions, and evaluating fractional derivatives. MATLAB includes the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egamma\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, but it accepts only real arguments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that evaluates the gamma function for complex arguments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53079,"title":"Easy Sequences 50: Blocked Gaussian Integers","description":"A Gaussian Integer is a complex number whose real and imaginary parts are both integers.\r\nA gaussian integer is said to be blocked with respect to another gaussian integer , if the line segment connecting and on the complex plane, pass through at least one more gaussian integer. In the figure below, where , the red colored points represents the blocked gaussian integers with respect to , While the green points represents unblocked gaussian integers.\r\n \r\nIn the above figure, blocked gaussian points, , and , are shown. These points lie within the a square with side lengths , in which is at the center. But these are not the only blocked gaussian points for this case. and are also blocked points. The sum total of all blocked gaussian integers relative to and bounded by the square with side and is .\r\nGiven a gaussian integer , centered at a square of side , find the absolute value of the sum of all blocked gaussian integers around , with respect to , that lies within the square (including, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: .\r\nPlease round-off your answer to 4 decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 722.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 361.25px; transform-origin: 407px 361.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Gaussian_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGaussian Integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 225px 8px; transform-origin: 225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a complex number whose real and imaginary parts are both integers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61px 8px; transform-origin: 61px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA gaussian integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAkCAYAAABixKGjAAAA00lEQVRIie2VQQ3DMAxFH4cwGIESKIIhCIMyKINRKIZBKIdQGIZSaA+2parKdkgcaarypKi3b+f7u4FO51YEYNavOxHYgbGF+BtYadB5QLp+egujok26Blho5HURA+Ljr7OUik8q8EH8PJ8NSBWNs2qBK1ELVg0vJzwgXQ81wjmCCjfJciJ/m2oWZL3dmahMxjdGHJKRw5Lx8BYOiBXRWxhkeLbiK44/pRdix3YqcF2cRKFlZxFb9V0FbbBWuPpG9vBuiF2WINfcB+QmM//0MHRuxAHmODh6hQd5nwAAAABJRU5ErkJggg==\" style=\"width: 11.5px; height: 18px;\" width=\"11.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42px 8px; transform-origin: 42px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is said to be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eblocked\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.5px 8px; transform-origin: 130.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with respect to another gaussian integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, if the line segment connecting \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAkCAYAAABixKGjAAAA00lEQVRIie2VQQ3DMAxFH4cwGIESKIIhCIMyKINRKIZBKIdQGIZSaA+2parKdkgcaarypKi3b+f7u4FO51YEYNavOxHYgbGF+BtYadB5QLp+egujok26Blho5HURA+Ljr7OUik8q8EH8PJ8NSBWNs2qBK1ELVg0vJzwgXQ81wjmCCjfJciJ/m2oWZL3dmahMxjdGHJKRw5Lx8BYOiBXRWxhkeLbiK44/pRdix3YqcF2cRKFlZxFb9V0FbbBWuPpG9vBuiF2WINfcB+QmM//0MHRuxAHmODh6hQd5nwAAAABJRU5ErkJggg==\" style=\"width: 11.5px; height: 18px;\" width=\"11.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.5px 8px; transform-origin: 311.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on the complex plane, pass through at least one more gaussian integer. In the figure below, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 63.5px; height: 18px;\" width=\"63.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the red colored points represents the blocked gaussian integers with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113px 8px; transform-origin: 113px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, While the green points represents unblocked gaussian integers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 404.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 202.25px; text-align: left; transform-origin: 384px 202.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the above figure, blocked gaussian points, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAkCAYAAAB15jFqAAABMUlEQVRYhe2WUZHDMAxEHwczKIEQCIIgCIMwKIOjEAyGEA6hYAylcPdha0buJbac5uvOO6Of1NYqWWlV6Oj46xhTDBfvOuthB6zA91u8gMWYY0t3dgvxIyV/J9TxZSDV50dLhQGY1bOB328+VfLMqfhqgVM6eKbfU5H6WjIrPGXNHLm+t2AlalqCNMhtpBYI6Xbwm4zXk/jVAg0jU0JIpEcyTOQNt99B+EjJAucyjLSNVhXSvaVmW2iYzxocsXmOtNTwivRjeGyWJm5WK66KhahjzfS1nlaPPsRsJITcsa5spWZCuME4JgPhQD468pbrFcKBWG2p5R2xsYRU6ykbaqNuqxnhTtToLAJ5h2o95U+AyRyEsLTAz3aqNoWdhtXnU/WW8OQz69T9j8alo6PjH+IHu6B/3OiYY/8AAAAASUVORK5CYII=\" style=\"width: 14.5px; height: 18px;\" width=\"14.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39px; height: 18px;\" width=\"39\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39px; height: 18px;\" width=\"39\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168px 8px; transform-origin: 168px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, are shown. These points lie within the a square with side lengths \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31px 8px; transform-origin: 31px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in which \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 63.5px; height: 18px;\" width=\"63.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.5px 8px; transform-origin: 256.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is at the center. But these are not the only blocked gaussian points for this case. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 49.5px; height: 18px;\" width=\"49.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 39px; height: 18px;\" width=\"39\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 258.5px 8px; transform-origin: 258.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are also blocked points. The sum total of all blocked gaussian integers relative to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 63.5px; height: 18px;\" width=\"63.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and bounded by the square with side \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 54px; height: 18px;\" width=\"54\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90px 8px; transform-origin: 90px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a gaussian integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, centered at a square of side \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33px 8px; transform-origin: 33px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eabsolute value of the sum\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51px 8px; transform-origin: 51px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e of all blocked gaussian integers around \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.5px 8px; transform-origin: 56.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95px 8px; transform-origin: 95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that lies within the square\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eincluding\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 153px; height: 18.5px;\" width=\"153\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease round-off your answer to 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function absSum = blockedGaussian(z,a)\r\n z = a;\r\nend","test_suite":"%%\r\nz = 3+2i; a = 9;\r\nabsSum_correct = 115.3776;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = 7-10i; a = 99;\r\nabsSum_correct = 45994.3016;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = -1-i; a = 999;\r\nabsSum_correct = 552493.6408;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = -4+5i; a = 9999;\r\nabsSum_correct = 250953396.5632;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = 10+i; a = 99999;\r\nabsSum_correct = 39401199538.8094;\r\nabsSum = blockedGaussian(z,a);\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = [1+2i 3-2i 7+7i]; a = 123456;\r\nabsSum_correct = [13362525603.2731 21546425116.3652 59158422678.1219];\r\nabsSum = blockedGaussian(z,a)\r\nassert(isequal(absSum,absSum_correct))\r\n%%\r\nz = arrayfun(@(x) x + i*(x-1)*(-1)^x,1:100); a = 7777;\r\nstat_correct = [1677439212.6962 1677263085.6360 23718896.0000 972842722.3354];\r\nabsSum = blockedGaussian(z,a);\r\nstat = round([mean(absSum) median(absSum) mode(absSum) std(absSum)],4);\r\nassert(isequal(stat,stat_correct))\r\n%%\r\nz = -123+456i; a = 2:2:2000;\r\nstat_correct = [247640834.4715 185966225.8317 0.0000 221359619.596];\r\nabsSum = arrayfun(@(b) blockedGaussian(z,b),a);\r\nstat = round([mean(absSum) median(absSum) mode(absSum) std(absSum)],4)\r\nassert(isequal(stat,stat_correct))\r\n%%\r\nfiletext = fileread('blockedGaussian.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2021-11-18T04:24:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-11-16T06:04:44.000Z","updated_at":"2025-10-07T14:22:21.000Z","published_at":"2021-11-17T07:50:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Gaussian_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGaussian Integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a complex number whose real and imaginary parts are both integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA gaussian integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is said to be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eblocked\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with respect to another gaussian integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, if the line segment connecting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e on the complex plane, pass through at least one more gaussian integer. In the figure below, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=3+2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the red colored points represents the blocked gaussian integers with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, While the green points represents unblocked gaussian integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the above figure, blocked gaussian points, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7+6i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, are shown. These points lie within the a square with side lengths \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, in which \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=3+2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is at the center. But these are not the only blocked gaussian points for this case. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-1-2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7+2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are also blocked points. The sum total of all blocked gaussian integers relative to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez=3+2i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and bounded by the square with side \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e96+64i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a gaussian integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, centered at a square of side \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eabsolute value of the sum\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e of all blocked gaussian integers around \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that lies within the square\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eincluding\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|\\\\ 96+64i\\\\ |=115.3776\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease round-off your answer to 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpeg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpeg\",\"contentType\":\"image/jpeg\",\"content\":\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAMxNAAAkpIAAgAAAAMxNAAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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