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Showing content from https://en.cppreference.com/w/cpp/language/../../c/language/../numeric/complex/cexp.html below:

cexpf, cexp, cexpl - cppreference.com

(1) (since C99) (2) (since C99) (3) (since C99)

#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.

[edit] Parameters [edit] Return value

If no errors occur, e raised to the power of z, \(\small e^z\)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 Â±0+0i, the result is 1+0i
If z is x+âi (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 +â+0i, the result is +â+0i
If z is -â+yi (for any finite y), the result is +0cis(y)
If z is +â+yi (for any finite nonzero y), the result is +âcis(y)
If z is -â+âi, the result is Â±0Â±0i (signs are unspecified)
If z is +â+âi, the result is Â±â+NaNi and FE_INVALID is raised (the sign of the real part is unspecified)
If z is -â+NaNi, the result is Â±0Â±0i (signs are unspecified)
If z is +â+NaNi, the result is Â±â+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)

[edit] Notes

The complex exponential function \(\small e^z\)ez for \(\small z = x + {\rm i}y\)z = x+iy equals \(\small e^x {\rm cis}(y)\)ex cis(y), or, \(\small e^x (\cos(y)+{\rm i}\sin(y))\)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:

[edit] 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)

[edit] See also

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