# cexpf, cexp, cexpl

< c‎ | numeric‎ | complex

C
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Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
 cexp clog
Trigonometric functions
Hyperbolic functions

 Defined in header  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  #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

### 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 ±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)

### 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)