NAME¶

std::pow(std::complex) - std::pow(std::complex)

Synopsis¶

Defined in header <complex>
template< class T > (1)
complex<T> pow( const complex<T>& x, const complex<T>& y );
template< class T > (2)
complex<T> pow( const complex<T>& x, const T& y );
template< class T > (3)
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>& (4) (since C++11)
y );
template< class T, class U > (5) (since C++11)
complex</*Promoted*/> pow( const complex<T>& x, const U& y );
template< class T, class U > (6) (since C++11)
complex</*Promoted*/> pow( const T& x, const complex<U>& y );

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> (since C++11)
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>

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¶

// 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)

See also¶

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