C++ Complex::norm() function

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The C++ std::complex::norm() function is used to return the squared magnitude of the complex number, calculated as the sum of the squares of its real and imaginary parts. For example, a=x+yi, where x and y are real and imaginary numbers, then the norm is calculated as a²+b².

Syntax

Following is the syntax for std::complex::norm() function.

norm (const complex<T>& x);
double norm (ArithmeticType x);

Parameters

• x − It indicates the complex value.

Return Value

It returns the norm value of the complex number x.

Exceptions

none

Example 1

In the following example, we are going to consider the basic usage of the norm() function.

#include <iostream>
#include <complex>
int main() {
   std::complex < double > a(1.1, 1.3);
   double x = std::norm(a);
   std::cout << "Result : " << x << std::endl;
   return 0;
}

Output

Output of the above code is as follows −

Result : 2.9

Example 2

Consider the following example, where we are going to use the norm() with the negative values.

#include <iostream>
#include <complex>
int main() {
   std::complex < double > x(-2.1, -3.2);
   double y = std::norm(x);
   std::cout << "Result : " << y << std::endl;
   return 0;
}

Output

Following is the output of the above code −

Result : 14.65

Example 3

In the following example, we are going to use the norm() on the real part.

#include <iostream>
#include <complex>
int main() {
   std::complex < double > a(2.3, 0.0);
   double b = std::norm(a);
   std::cout << "Result : " << b << std::endl;
   return 0;
}

Output

If we run the above code it will generate the following output −

Result : 5.29