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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 arg has type long double complex, cexpl is called. if arg has type double complex, cexp is called, if arg has type float complex, cexpf is called. If arg is real or integer, then the macro invokes the corresponding real function (expf, exp, expl)

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]