cexpf, cexp, cexpl
Header: <complex.h>
1-3) Computes the complex base-e exponential of z.
# Declarations
float complex cexpf( float complex z );
(since C99)
double complex cexp( double complex z );
(since C99)
long double complex cexpl( long double complex z );
(since C99)
#define exp( z )
(since C99)
# Parameters
z: complex argument
# Return value
If no errors occur, e raised to the power of z, (\small e^z)ez is returned.
# Notes
The complex exponential function (\small e^z)ez for (\small z = x + {\rm i}y)z = x+iy equals (\small e^x {\rm cis}(y))ex cis(y), or, (\small e^x (\cos(y)+{\rm i}\sin(y)))ex (cos(y) + i sin(y))
The exponential function is an entire function in the complex plane and has no branch cuts.
# Example
#include <stdio.h>
#include <math.h>
#include <complex.h>
int main(void)
{
double PI = acos(-1);
double complex z = cexp(I * PI); // Euler's formula
printf("exp(i*pi) = %.1f%+.1fi\n", creal(z), cimag(z));
}