cexpf, cexp, cexpl

From cppreference.com
< clrm; | numericlrm; | 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.

Parameters

z - complex argument

Return value

If no errors occur, e raised to the power of z, ez
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 00i (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 00i (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)

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.

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

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

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