Convert a Complex Number to exponential real

Hi

I am looking for help to calculate value of a complex number say x = 2 +1j*5 using exponential function

Thanks you

Answer 1

[Robert U]

Hi Jogger,

have a look at Euler's formula (https://en.wikipedia.org/wiki/Euler's_formula).

x = 2 + 1j * 5;
r = sqrt(real(x)^2 + imag(x)^2);
phi = atan2(imag(x),real(x));
fprintf(1,'z = r * exp(j*phi)\nr = %.2f\nphi = %.2f',r,phi)

z = r * exp(j*phi)
r = 5.39
phi = 1.19

Kind regards,

Robert

Answer 2

[dpb]

MATLAB has builtin functions abs (or hypot()) and angle() for the above explicit implementations...

>> x=complex(2,5);

>> cmplx2exp=@(x) deal(abs(x),angle(x));

>> [r,theta]=cmplx2exp(x)
r =
    5.3852
theta =
    1.1903
>> 

[Life is Wonderful]

Thanks a lot Robert U and dpb

I make it little simpler

x = pi;
% complex number 
(1) exp(1i*pi)
  -1.0000 + 0.0000i
  OR 
% complex number   
(1) exp(complex(0,pi))
-1.0000 + 0.0000i  
% Real number 
(2) exp(pi)
   23.1407
% Side note, exponential is inverse of logarithm 
>> log(23.1407)

ans =

    3.1416 % get  back the input value

I want to know how exp(1i*pi) is mapped to exp(pi) so that I know the input value is same !

OR

convert multivalue to single value . By doing , one can determine logarithm ( single value )

Thanks

[Life is Wonderful]

I have written a script and can someone explain the correctness

x = [-2*pi:1:2*pi];
y = exp(x);
z = log(y);
y1= exp(1i*x) ;
z1= (log(1i*y1));
    fprintf('%10s\t| %10s\t|%10s\t| %15s%+15s| %15s%+15s|\n------------+---------------+-----------+---------------+---------------+---------------+---------------+\n','x(i)', 'exp(i)', 'log(i)', 'expreal(y1(i))','expimag(y1(i))','logreal(z1(i))','logimag(z1(i))');
for i = 1:length(x)
    fprintf('%10f\t| %10.5f\t|%10f\t| %15f%+15f| %15f%+15f|\n',x(i), y(i), z(i), real(y1(i)),imag(y1(i)),real(z1(i)),imag(z1(i)));
end

[Life is Wonderful]

I ma having following output

      x(i)	|     exp(i)	|    log(i)	|  expreal(y1(i)) expimag(y1(i))|  logreal(z1(i)) logimag(z1(i))|
----------------+---------------+---------------+---------------+---------------+---------------+---------------+
 -6.283185	|    0.00187	| -6.283185	|        1.000000      +0.000000|        0.000000      +1.570796|
 -5.283185	|    0.00508	| -5.283185	|        0.540302      +0.841471|       -0.000000      +2.570796|
 -4.283185	|    0.01380	| -4.283185	|       -0.416147      +0.909297|        0.000000      -2.712389|
 -3.283185	|    0.03751	| -3.283185	|       -0.989992      +0.141120|        0.000000      -1.712389|
 -2.283185	|    0.10196	| -2.283185	|       -0.653644      -0.756802|       -0.000000      -0.712389|
 -1.283185	|    0.27715	| -1.283185	|        0.283662      -0.958924|       -0.000000      +0.287611|
 -0.283185	|    0.75338	| -0.283185	|        0.960170      -0.279415|       -0.000000      +1.287611|
  0.716815	|    2.04790	|  0.716815	|        0.753902      +0.656987|        0.000000      +2.287611|
  1.716815	|    5.56677	|  1.716815	|       -0.145500      +0.989358|        0.000000      -2.995574|
  2.716815	|   15.13205	|  2.716815	|       -0.911130      +0.412118|       -0.000000      -1.995574|
  3.716815	|   41.13316	|  3.716815	|       -0.839072      -0.544021|       -0.000000      -0.995574|
  4.716815	|  111.81153	|  4.716815	|        0.004426      -0.999990|        0.000000      +0.004426|
  5.716815	|  303.93525	|  5.716815	|        0.843854      -0.536573|       -0.000000      +1.004426|