# std::pow(std::complex)

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< cpp‎ | numeric‎ | complex

Defined in header `<complex>` |  |
template< class T > std::complex <T> pow( const std::complex <T>& x, int y ); | (1) | (until C++11)
template< class T > std::complex <T> pow( const std::complex <T>& x, const std::complex <T>& y ); | (2) |
template< class T > std::complex <T> pow( const std::complex <T>& x, const T& y ); | (3) |
template< class T > std::complex <T> pow( const T& x, const std::complex <T>& y ); | (4) |
Additional overloads (since C++11) |  |
Defined in header `<complex>` |  |
| (A) |
template< class T1, class T2 > std::complex </* common-type */> pow( const std::complex <T1>& x, const std::complex <T2>& y ); |  | (until C++23)
template< class T1, class T2 > std::complex < std::common_type_t <T1, T2>> pow( const std::complex <T1>& x, const std::complex <T2>& y ); |  | (since C++23)
| (B) |
template< class T, class NonComplex > std::complex </* common-type */> pow( const std::complex <T>& x, const NonComplex& y ); |  | (until C++23)
template< class T, class NonComplex > std::complex < std::common_type_t <T, NonComplex>> pow( const std::complex <T>& x, const NonComplex& y ); |  | (since C++23)
| (C) |
template< class T, class NonComplex > std::complex </* common-type */> pow( const NonComplex& x, const std::complex <T>& y ); |  | (until C++23)
template< class T, class NonComplex > std::complex < std::common_type_t <T, NonComplex>> pow( const NonComplex& x, const std::complex <T>& y ); |  | (since C++23)

1-4) Computes complex x raised to a complex power y with a branch cut along the negative real axis for the first argument. Non-complex arguments are treated as complex numbers with positive zero imaginary component.

A-C) Additional overloads are provided. `NonComplex` is not a specialization of std::complex. | (since C++11)

### Parameters

x | - | base
y | - | exponent

### Return value

1-4) If no errors occur, the complex power xy
, is returned.
Errors and special cases are handled as if the operation is implemented by std::exp (y * std::log (x)).
The result of std::pow (0, 0) is implementation-defined.
A-C) Same as (2-4).

### Notes

Overload (1) was provided in C++98 to match the extra overloads (2) of std::pow. Those overloads were removed by the resolution of LWG issue 550, and overload (1) was removed by the resolution of LWG issue 844.

The additional overloads are not required to be provided exactly as (A-C). They only need to be sufficient to ensure that for their first argument base and second argument exponent:

If base and/or exponent has type std::complex <T>:

- If base and/or exponent has type std::complex <long double> or long double, then `std::pow(base, exponent)` has the same effect as `std::pow`( std::complex <long double>(base),
  std::complex <long double>(exponent)).
- Otherwise, if base and/or exponent has type std::complex <double>, double, or an integer type, then `std::pow(base, exponent)` has the same effect as `std::pow`( std::complex <double>(base),
  std::complex <double>(exponent)).
- Otherwise, if base and/or exponent has type std::complex <float> or float, then `std::pow(base, exponent)` has the same effect as `std::pow`( std::complex <float>(base),
  std::complex <float>(exponent)).

(until C++23)

If one argument has type std::complex <T1> and the other argument has type `T2` or std::complex <T2>, then `std::pow(base, exponent)` has the same effect as `std::pow`( std::complex < std::common_type_t <T1, T2>>(base), std::complex < std::common_type_t <T1, T2>>(exponent)). If std::common_type_t <T1, T2> is not well-formed, then the program is ill-formed. | (since C++23)

### Example

Run this code

    #include <complex>
    #include <iostream>

    int main()
    {
        std::cout << std::fixed;

        std::complex<double> z(1.0, 2.0);
        std::cout << "(1,2)^2 = " << std::pow(z, 2) << '\n';

        std::complex<double> z2(-1.0, 0.0); // square root of -1
        std::cout << "-1^0.5 = " << std::pow(z2, 0.5) << '\n';

        std::complex<double> z3(-1.0, -0.0); // other side of the cut
        std::cout << "(-1,-0)^0.5 = " << std::pow(z3, 0.5) << '\n';

        std::complex<double> i(0.0, 1.0); // i^i = exp(-pi / 2)
        std::cout << "i^i = " << std::pow(i, i) << '\n';
    }

Output:

    (1,2)^2 = (-3.000000,4.000000)
    -1^0.5 = (0.000000,1.000000)
    (-1,-0)^0.5 = (0.000000,-1.000000)
    i^i = (0.207880,0.000000)

### See also

sqrt(std::complex) | complex square root in the range of the right half-plane (function template)
powpowfpowl (C++11)(C++11) | raises a number to the given power (\(\small{x^y}\)xy) (function)
pow(std::valarray) | applies the function std::pow to two valarrays or a valarray and a value (function template)
C documentation for cpow

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