std::pow(std::complex)

C++

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
exp
log
log10
Power functions
pow
sqrt
Trigonometric functions
sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

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>

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	raises a number to the given power (xy) (function)
pow(std::valarray)	applies the function std::pow to two valarrays or a valarray and a value (function template)