std::pow(std::complex) (3) Linux Manual Page

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>
(4)(since C++ 11)

    complex</*Promoted*/> pow(const complex<T> &x, const complex<U> &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

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