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Showing content from https://en.cppreference.com/w/cpp/algorithm/../ranges/../numeric/complex/norm.html below:

std::norm(std::complex) - cppreference.com

(1) (until C++20) template< class T > constexpr T norm( const std::complex<T>& z ); (since C++20) (A) float norm( float f ); double norm( double f ); long double norm( long double f ); (until C++20) constexpr float norm( float f ); constexpr double norm( double f ); constexpr long double norm( long double f ); (since C++20)
(until C++23)

template< class FloatingPoint > constexpr FloatingPoint norm( FloatingPoint f );

(since C++23) (B)

template< class Integer > double norm( Integer i );

(until C++20)

template< class Integer > constexpr double norm( Integer i );

(since C++20)

1) Returns the squared magnitude of the complex number z.

A,B) Additional overloads are provided for all integer and floating-point types, which are treated as complex numbers with zero imaginary component.

(since C++11) [edit] Parameters z - complex value f - floating-point value i - integer value [edit] Return value

1) The squared magnitude of z.

A) The square of f.

B) The square of i.

[edit] Notes

The norm calculated by this function is also known as field norm or absolute square.

The Euclidean norm of a complex number is provided by std::abs, which is more costly to compute. In some situations, it may be replaced by std::norm, for example, if abs(z1) > abs(z2) then norm(z1) > norm(z2).

The additional overloads are not required to be provided exactly as (A,B). They only need to be sufficient to ensure that for their argument num:

If num has a standard(until C++23) floating-point type T, then std::norm(num) has the same effect as std::norm(std::complex<T>(num)).
Otherwise, if num has an integer type, then std::norm(num) has the same effect as std::norm(std::complex<double>(num)).

[edit] Example

#include <cassert>
#include <complex>
#include <iostream>
 
int main()
{
    constexpr std::complex<double> z {3.0, 4.0};
    static_assert(std::norm(z) == (z.real() * z.real() + z.imag() * z.imag()));
    static_assert(std::norm(z) == (z * std::conj(z)));
           assert(std::norm(z) == (std::abs(z) * std::abs(z)));
    std::cout << "std::norm(" << z << ") = " << std::norm(z) << '\n';
}

Output:

[edit] See also returns the magnitude of a complex number
(function template) [edit] returns the complex conjugate
(function template) [edit] constructs a complex number from magnitude and phase angle
(function template) [edit]

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