cexpf, cexp, cexpl

float complex       cexpf( float complex z );

double complex      cexp( double complex z );

long double complex cexpl( long double complex z );

#define exp( z )

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

• C11 standard (ISO/IEC 9899:2011):
• 7.3.7.1 The cexp functions (p: 194)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• G.6.3.1 The cexp functions (p: 543)
• G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
• 7.3.7.1 The cexp functions (p: 176)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• G.6.3.1 The cexp functions (p: 478)
• G.7 Type-generic math <tgmath.h> (p: 480)

See also