Defined in header <complex>
template< class T > 
T norm( const complex<T>& z );
long double norm( long double z );
(2) (since C++11)
template< class DoubleOrInteger >
double norm( DoubleOrInteger z );
(3) (since C++11)
float norm( float z );
(4) (since C++11)

Returns the squared magnitude of the complex number z.

(since C++11)Additional overloads are provided for float, double, long double, and all integer types, which are treated as complex numbers with zero imaginary component.


z - complex value

Return value

the squared magnitude of z.


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).

See also

returns the magnitude of a complex number
(function template)
returns the complex conjugate
(function template)
constructs a complex number from magnitude and phase angle
(function template)

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