abs

Absolute value of a complex number

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Contents

Interface
Description
Note
Page Comments

Interface

#include <complex> double  abs (complex<T> z)

Description

The abs function returns the absolute value of the complex number $\inline z = a + {\rm i} b$ . The result is the real number denoted by $\inline |z|$ and defined through:

$|z| = \sqrt{a^2+b^2}$

(2)

Example:

Example - Abs

Problem

This program returns the absolute value of the complex number z=0.5+2i.

Workings

#include <stdio.h>
#include <complex>
 
using std::complex;
 
int main()
{
  complex<double> z;
  z=0.5+2i;
  printf("|0.5 + 2 i| = %.4lf\n", abs(z));
  return 0;
}

Solution

Output:

|0.5 + 2 i| = 2.0616

Note

The function is actually an alias for hypot(a, b) = $\inline \sqrt{a^2 + b^2}$ .