# cpowf, cpow, cpowl

< c‎ | numeric‎ | complex

Complex number arithmetic
Types and the imaginary constant
 complex(C99) _Complex_I(C99) CMPLX(C11)
 imaginary(C99) _Imaginary_I(C99) I(C99)
Manipulation
 cimag(C99) creal(C99) carg(C99)
 cabs(C99) conj(C99) cproj(C99)
Power and exponential functions
 cexp(C99) clog(C99)
 cpow(C99) csqrt(C99)
Trigonometric functions
 ccos(C99) csin(C99) ctan(C99)
 cacos(C99) casin(C99) catan(C99)
Hyperbolic functions
 ccosh(C99) csinh(C99) ctanh(C99)
 cacosh(C99) casinh(C99) catanh(C99)

 Defined in header  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  #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.

## Contents

### 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

#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)