std::pow(std::complex) - cppreference.com

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# std::pow(std::complex)

From cppreference.com
< cpp‎ | numeric‎ | complex

Defined in header `<complex>` |  |
template< class T > complex<T> pow( const complex<T>& x, const complex<T>& y); |  |
template< class T > complex<T> pow( const complex<T>& x, const T& y); |  |
template< class T > complex<T> pow( const T& x, const complex<T>& y); |  |
template< class T, class U > complex</*Promoted*/> pow( const complex<T>& x, const complex<U>& y); |  | (since C++11)
template< class T, class U > complex</*Promoted*/> pow( const complex<T>& x, const U& y); |  | (since C++11)
template< class T, class U > complex</*Promoted*/> pow( const T& x, const complex<U>& y); |  | (since C++11)

Computes complex `x` raised to a complex power `y` with a branch cut along the negative real axis for the first argument.

(since C++11)Additional overloads are provided for all arithmetic types, such that

  1. If either argument is long double or std::complex<long double>, then both arguments are cast to std::complex<long double>
  2. Otherwise, if either argument is double, std::complex<double> or integer type, then both arguments are cast to std::complex<double>
  3. Otherwise, if either argument is float or std::complex<float>, then both arguments are cast to std::complex<float>

### [edit] Parameters

x | - | base as a complex value
y | - | exponent as a complex value

### [edit] 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 std::exp(y*std::log(x))

The result of std::pow(0, 0) is implementation-defined.

### [edit] Example

Run this code

    #include <iostream>
    #include <complex>

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

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

        std::complex<double> z2(-1, 0);  // square root of -1
        std::cout << "-1^0.5 = " << std::pow(z2, 0.5) << '\n';

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

        std::complex<double> i(0, 1); // 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)

### [edit] See also

sqrt(std::complex) | complex square root in the range of the right half-plane (function template) [edit]
pow | raises a number to the given power (xy) (function) [edit]
pow(std::valarray) | applies the function std::pow to two valarrays or a valarray and a value (function template) [edit]
C documentation for cpow

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