cexpf, cexp, cexpl

Parameters

Return value

If no errors occur, e raised to the power of z , \(\small e^z\) e z
is returned.

Error handling and special values

Errors are reported consistent with math_errhandling .

If the implementation supports IEEE floating-point arithmetic,

• cexp ( conj ( z ) ) == conj ( cexp ( z ) )
• If z is ±0+0i , the result is 1+0i
• If z is x+∞i (for any finite x), the result is NaN+NaNi and FE_INVALID is raised.
• If z is x+NaNi (for any finite x), the result is NaN+NaNi and FE_INVALID may be raised.
• If z is +∞+0i , the result is +∞+0i
• If z is -∞+yi (for any finite y), the result is +0cis(y)
• If z is +∞+yi (for any finite nonzero y), the result is +∞cis(y)
• If z is -∞+∞i , the result is ±0±0i (signs are unspecified)
• If z is +∞+∞i , the result is ±∞+NaNi and FE_INVALID is raised (the sign of the real part is unspecified)
• If z is -∞+NaNi , the result is ±0±0i (signs are unspecified)
• If z is +∞+NaNi , the result is ±∞+NaNi (the sign of the real part is unspecified)
• If z is NaN+0i , the result is NaN+0i
• If z is NaN+yi (for any nonzero y), the result is NaN+NaNi and FE_INVALID may be raised
• If z is NaN+NaNi , the result is NaN+NaNi

where \(\small{\rm cis}(y)\) cis(y) is \(\small \cos(y)+{\rm i}\sin(y)\) cos(y) + i sin(y)

Notes

The complex exponential function \(\small e^z\) e z
for \(\small z = x + {\rm i}y\) z = x+iy equals \(\small e^x {\rm cis}(y)\) e x
cis(y) , or, \(\small e^x (\cos(y)+{\rm i}\sin(y))\) e x
(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));
}

exp(i*pi) = -1.0+0.0i

References