# cexpf, cexp, cexpl

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< 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.

### 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 `+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)

### 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

Run this code

    #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

clog clogf clogl (C99)(C99)(C99) | computes the complex natural logarithm (function)
exp expf expl (C99)(C99) | computes e raised to the given power (ex) (function)
C++ documentation for exp

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