how to transform a complex equation to a trigonometric function form?

I have a complex equation like this-(5746772847587216969320685600118169822982082276949701951610533185511*exp((72904590186540958068117318959024937034055680*x*i)/14834859346081795520881636801061155781141830677))/23147970522987067069884769431432445012502993199558109347048325120000 + (41599612658116695904845876729613416447229334433995796300250749185439*exp((137752303494633663599702993999275021398179840*x*i)/14834859346081795520881636801061155781141830677))/4629594104597413413976953886286489002500598639911621869409665024000 + (28362175122705238373636542692374717152762842256598930556679573043671*(1/exp((5583316590711408616116494615509809860968448*x*i)/5017673014115901297250206286887358756475835969)))/23147970522987067069884769431432445012502993199558109347048325120000 - (18384791256775548276066453844694518962850997062684442545274081216559*exp((16350468792908182397149333533303040032899072*x*i)/5017673014115901297250206286887358756475835969))/4629594104597413413976953886286489002500598639911621869409665024000=0

Now,I'm trying to reform it into a trigonometric function form so that I can get the real & imaginary part. who konws how?

Answer 1

[Star Strider]

The rewrite function can use the Euler identities to convert the complex exponential to the trigonometric form you want:

syms x 
f = (5746772847587216969320685600118169822982082276949701951610533185511*exp((72904590186540958068117318959024937034055680*x*i)/14834859346081795520881636801061155781141830677))/23147970522987067069884769431432445012502993199558109347048325120000 + (41599612658116695904845876729613416447229334433995796300250749185439*exp((137752303494633663599702993999275021398179840*x*i)/14834859346081795520881636801061155781141830677))/4629594104597413413976953886286489002500598639911621869409665024000 + (28362175122705238373636542692374717152762842256598930556679573043671*(1/exp((5583316590711408616116494615509809860968448*x*i)/5017673014115901297250206286887358756475835969)))/23147970522987067069884769431432445012502993199558109347048325120000 - (18384791256775548276066453844694518962850997062684442545274081216559*exp((16350468792908182397149333533303040032899072*x*i)/5017673014115901297250206286887358756475835969))/4629594104597413413976953886286489002500598639911621869409665024000;

f = rewrite(f, 'sincos')
Ref = simplify(collect(real(f)))        % Real part
Imf = simplify(collect(imag(f)))        % Imaginary part

[Pavel Podder]

thank u

[Star Strider]

My pleasure!

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