std::pow(std::complex)(3)

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

Synopsis
   Defined in header <complex>
   template< class T > (until
   std::complex<T> pow( const std::complex<T>& x, (1) C++11)
   int y );
   template< class T >
   std::complex<T> pow( const std::complex<T>& x, (2)
   const std::complex<T>& y );
   template< class T >
   std::complex<T> pow( const std::complex<T>& x, (3)
   const T& y );
   template< class T >
   std::complex<T> pow( const T& x, const (4)
   std::complex<T>& y );
   Additional overloads (since C++11)
   Defined in header <complex>
   template< class T1, class T2 >
   std::complex</* common-type */> (until
                        C++23)
       pow( const std::complex<T1>& x, const
   std::complex<T2>& y );
   template< class T1, class T2 >
   std::complex<std::common_type_t<T1, T2>> (since
                        C++23)
       pow( const std::complex<T1>& x, const
   std::complex<T2>& y );
   template< class T, class NonComplex >
   std::complex</* common-type */> (until
                        C++23)
       pow( const std::complex<T>& x, const
   NonComplex& y ); (A)
   template< class T, class NonComplex >
   std::complex<std::common_type_t<T, NonComplex>> (since
                        C++23)
       pow( const std::complex<T>& x, const
   NonComplex& y ); (B)
   template< class T, class NonComplex >
   std::complex</* common-type */> (until
                        C++23)
       pow( const NonComplex& x, const
   std::complex<T>& y ); (C)
   template< class T, class NonComplex >
   std::complex<std::common_type_t<T, NonComplex>> (since
                        C++23)
       pow( const NonComplex& x, const
   std::complex<T>& y );
   1-4) Computes complex x raised to a complex power y with a branch cut along the
   negative real axis for the first argument. Non-complex arguments are treated as
   complex numbers with positive zero imaginary component.
   A-C) Additional overloads are provided. NonComplex is not a (since C++11)
   specialization of std::complex.

Parameters
   x - base
   y - exponent

Return value
   1-4) 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.
   A-C) Same as (2-4).

Notes
   Overload (1) was provided in C++98 to match the extra overloads (2) of std::pow.
   Those overloads were removed by the resolution of LWG issue 550, and overload (1)
   was removed by the resolution of LWG issue 844.
   The additional overloads are not required to be provided exactly as (A-C). They only
   need to be sufficient to ensure that for their first argument base and second
   argument exponent:
   If base and/or exponent has type std::complex<T>:
     * If base and/or exponent has type std::complex<long double> or long
       double, then std::pow(base, exponent) has the same effect as
       std::pow(std::complex<long double>(base),
                std::complex<long double>(exponent)).
     * Otherwise, if base and/or exponent has type std::complex<double>, (until C++23)
       double, or an integer type, then std::pow(base, exponent) has the
       same effect as std::pow(std::complex<double>(base),
                std::complex<double>(exponent)).
     * Otherwise, if base and/or exponent has type std::complex<float> or
       float, then std::pow(base, exponent) has the same effect as
       std::pow(std::complex<float>(base),
                std::complex<float>(exponent)).
   If one argument has type std::complex<T1> and the other argument has
   type T2 or std::complex<T2>, then std::pow(base, exponent) has the
   same effect as std::pow(std::complex<std::common_type_t<T1,
   T2>>(base), (since C++23)
            std::complex<std::common_type_t<T1, T2>>(exponent)).
   If std::common_type_t<T1, T2> is not well-formed, then the program is
   ill-formed.

Example
// Run this code
 #include <complex>
 #include <iostream>
 int main()
 {
     std::cout << std::fixed;
     std::complex<double> z(1.0, 2.0);
     std::cout << "(1,2)^2 = " << std::pow(z, 2) << '\n';
     std::complex<double> z2(-1.0, 0.0); // square root of -1
     std::cout << "-1^0.5 = " << std::pow(z2, 0.5) << '\n';
     std::complex<double> z3(-1.0, -0.0); // other side of the cut
     std::cout << "(-1,-0)^0.5 = " << std::pow(z3, 0.5) << '\n';
     std::complex<double> i(0.0, 1.0); // 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)
   C documentation for
   cpow