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std::pow(std::complex)

Defined in header <complex>
template< class T >
complex<T> pow( const complex<T>& x, const complex<T>& y );
(1)
template< class T >
complex<T> pow( const complex<T>& x, const T& y );
(2)
template< class T >
complex<T> pow( const T& x, const complex<T>& y );
(3)
template< class T, class U >
complex</*Promoted*/> pow( const complex<T>& x, const complex<U>& y );
(4) (since C++11)
template< class T, class U >
complex</*Promoted*/> pow( const complex<T>& x, const U& y );
(5) (since C++11)
template< class T, class U >
complex</*Promoted*/> pow( const T& x, const complex<U>& y );
(6) (since C++11)
1-3) Computes complex x raised to a complex power y with a branch cut along the negative real axis for the first argument.
4-6) 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>
(since C++11)

Parameters

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

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.

Example

#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)

See also

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

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