std::pow(std::complex)

 

C++

Compiler support

Freestanding and hosted

Language

Standard library

Standard library headers

Named requirements

Feature test macros (C++20)

Language support library

Concepts library (C++20)

Metaprogramming library (C++11)

Diagnostics library

General utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (C++17)

Regular expressions library (C++11)

Concurrency support library (C++11)

Execution support library (C++26)

Technical specifications

Symbols index

External libraries

 

Numerics library

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
gcd (C++17)	lcm (C++17)
Interpolations
midpoint (C++20)	lerp (C++20)
Saturation arithmetic
add_sat (C++26) sub_sat (C++26) saturate_cast (C++26)	mul_sat (C++26) div_sat (C++26)
Generic numeric operations
iota (C++11) ranges::iota (C++23) accumulate inner_product adjacent_difference partial_sum	reduce (C++17) transform_reduce (C++17) inclusive_scan (C++17) exclusive_scan (C++17) transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
Bit operations
has_single_bit (C++20)     bit_cast (C++20) bit_ceil (C++20) bit_floor (C++20) bit_width (C++20) rotl (C++20) rotr (C++20)	popcount (C++20) countl_zero (C++20) countl_one (C++20) countr_zero (C++20) countr_one (C++20) byteswap (C++23) endian (C++20)

 

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!= (until C++20)   operator<<operator>> get(std::complex) (C++26)	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
log   log10   exp
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)
Helper types
tuple_size<std::complex> (C++26)
tuple_element<std::complex> (C++26)

 

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

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)
powpowfpowl (C++11)(C++11)	raises a number to the given power (\(\small{x^y}\)xy) (function)
pow(std::valarray)	applies the function std::pow to two valarrays or a valarray and a value (function template)
C documentation for cpow