# cpowf, cpow, cpowl

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< c‎ | numeric‎ | complex

Defined in header `<complex.h>` |  |
float complex cpowf( float complex x, float complex y ); | (1) | (since C99)
double complex cpow( double complex x, double complex y ); | (2) | (since C99)
long double complex cpowl( long double complex x, long double complex y ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define pow( x, y ) | (4) | (since C99)

1-3) Computes the complex power function xy
, with branch cut for the first parameter along the negative real axis.
4) Type-generic macro: If any argument has type long double complex, `cpowl` is called. if any argument has type double complex, `cpow` is called, if any argument has type float complex, `cpowf` is called. If the arguments are real or integer, then the macro invokes the corresponding real function (powf, pow, powl). If any argument is imaginary, the corresponding complex number version is called.

### Parameters

x, y | - | complex argument

### Return value

If no errors occur, the complex power xy
, is returned.

Errors and special cases are handled as if the operation is implemented by cexp(y*clog(x)), except that the implementation is allowed to treat special cases more carefully.

### Example

Run this code

    #include <stdio.h>
    #include <complex.h>

    int main(void)
    {
        double complex z = cpow(1.0+2.0*I, 2);
        printf("(1+2i)^2 = %.1f%+.1fi\n", creal(z), cimag(z));

        double complex z2 = cpow(-1, 0.5);
        printf("(-1+0i)^0.5 = %.1f%+.1fi\n", creal(z2), cimag(z2));

        double complex z3 = cpow(conj(-1), 0.5); // other side of the cut
        printf("(-1-0i)^0.5 = %.1f%+.1fi\n", creal(z3), cimag(z3));

        double complex z4 = cpow(I, I); // i^i = exp(-pi/2)
        printf("i^i = %f%+fi\n", creal(z4), cimag(z4));
    }

Output:

    (1+2i)^2 = -3.0+4.0i
    (-1+0i)^0.5 = 0.0+1.0i
    (-1-0i)^0.5 = 0.0-1.0i
    i^i = 0.207880+0.000000i

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.3.8.2 The cpow functions (p: 195-196)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - G.6.4.1 The cpow functions (p: 544)

  - G.7 Type-generic math <tgmath.h> (p: 545)

- C99 standard (ISO/IEC 9899:1999):

  - 7.3.8.2 The cpow functions (p: 177)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - G.6.4.1 The cpow functions (p: 479)

  - G.7 Type-generic math <tgmath.h> (p: 480)

### See also

csqrt csqrtf csqrtl (C99)(C99)(C99) | computes the complex square root (function)
pow powf powl (C99)(C99) | computes a number raised to the given power (xy) (function)
C++ documentation for pow

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