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cexpf, cexp, cexpl

From cppreference.com
< c‎ | numeric‎ | complex
Defined in header <complex.h>
float complex       cexpf( float complex z );
(1) (since C99)
double complex      cexp( double complex z );
(2) (since C99)
long double complex cexpl( long double complex z );
(3) (since C99)
Defined in header <tgmath.h>
#define exp( z )
(4) (since C99)
1-3) Computes the complex base-e exponential of z.
4) Type-generic macro: If z has type long double complex, cexpl is called. if z has type double complex, cexp is called, if z has type float complex, cexpf is called. If z is real or integer, then the macro invokes the corresponding real function (expf, exp, expl). If z is imaginary, the corresponding complex argument version is called.

Contents

[edit] Parameters

z - complex argument

[edit] Return value

If no errors occur, e raised to the power of z, ez
is returned.

[edit] 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 +0+cis(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 cis(y) is cos(y) + i sin(y)

[edit] Notes

The complex exponential function ez
for z = x+iy equals to ex
cis(y)
, or, ex
(cos(y) + i sin(y))

The exponential function is an entire function in the complex plane and has no branch cuts.

[edit] 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));
 
}

Output:

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

[edit] See also

(C99)(C99)(C99)
computes the complex natural logarithm
(function) [edit]
(C99)(C99)
computes e raised to the given power (ex)
(function) [edit]