Modulus of a Complex Number (original) (raw)

Last Updated : 12 Jul, 2025

Given a complex number z, the task is to determine the modulus of this complex number. Note: Given a complex number z = a + ib the modulus is denoted by |z| and is defined as [latex]\left | z \right | = \sqrt{a^{2}+b^{2}}[/latex] Examples:

Input: z = 3 + 4i
Output: 5 |z| = (32 + 42)1/2 = (9 + 16)1/2 = 5

Input: z = 6 - 8i
Output: 10
Explanation: |z| = (62 + (-8)2)1/2 = (36 + 64)1/2 = 10

Approach: For the given complex number z = x + iy:

1. Find the real and imaginary parts, x and y respectively.

If z = x +iy

Real part = x Imaginary part = y

1. Find the square of x and y separately.

Square of Real part = x2 Square of Imaginary part = y2

1. Find the sum of the computed squares.

Sum = Square of Real part + Square of Imaginary part = x2 + y2

1. Find the square root of the computed sum. This will be the modulus of the given complex number

[latex]\left | z \right | = \sqrt{x^{2}+y^{2}}[/latex]

Below is the implementation of the above approach:

C++ `

// C++ program to find the // Modulus of a Complex Number

#include <bits/stdc++.h> using namespace std;

// Function to find modulus // of a complex number void findModulo(string s) { int l = s.length(); int i, modulus = 0;

// Storing the index of '+'
if (s.find('+') < l) {
    i = s.find('+');
}
// Storing the index of '-'
else {
    i = s.find('-');
}

// Finding the real part
// of the complex number
string real = s.substr(0, i);

// Finding the imaginary part
// of the complex number
string imaginary = s.substr(i + 1, l - 1);

int x = stoi(real);
int y = stoi(imaginary);

cout << sqrt(x * x + y * y) << "\n";

}

// Driver code int main() { string s = "3+4i";

findModulo(s);

return 0;

}

Java

// Java program to find the // Modulus of a Complex Number import java.util.*;

class GFG{

// Function to find modulus // of a complex number static void findModulo(String s) { int l = s.length(); int i, modulus = 0;

// Storing the index of '+'
if (s.contains("+")) {
    i = s.indexOf("+");
}

// Storing the index of '-'
else {
    i = s.indexOf("-");
}

// Finding the real part
// of the complex number
String real = s.substring(0, i);

// Finding the imaginary part
// of the complex number
String imaginary = s.substring(i + 1, l-1);

int x = Integer.parseInt(real);
int y = Integer.parseInt(imaginary);

System.out.print(Math.sqrt(x * x + y * y)+ "\n");

}

// Driver code public static void main(String[] args) { String s = "3+4i";

findModulo(s);

} }

// This code is contributed by Rajput-Ji

Python 3

Python 3 program to find the

Modulus of a Complex Number

from math import sqrt

Function to find modulus

of a complex number

def findModulo(s): l = len(s) modulus = 0

# Storing the index of '+'
if ( '+' in s ):
    i = s.index('+')

# Storing the index of '-'
else:
    i = s.index('-')

# Finding the real part
# of the complex number
real = s[0:i]

# Finding the imaginary part
# of the complex number
imaginary = s[i + 1:l - 1]

x = int(real)
y = int(imaginary)

print(int(sqrt(x * x + y * y)))

Driver code

if name == 'main': s = "3+4i"

findModulo(s)

This code is contributed by Surendra_Gangwar

C#

// C# program to find the // Modulus of a Complex Number using System;

public class GFG{

// Function to find modulus // of a complex number static void findModulo(String s) { int l = s.Length; int i;

// Storing the index of '+'
if (s.Contains("+")) {
    i = s.IndexOf("+");
}

// Storing the index of '-'
else {
    i = s.IndexOf("-");
}

// Finding the real part
// of the complex number
String real = s.Substring(0, i);

// Finding the imaginary part
// of the complex number
String imaginary = s.Substring(i + 1, l-i - 2);

int x = Int32.Parse(real);
int y = Int32.Parse(imaginary);

Console.Write(Math.Sqrt(x * x + y * y)+ "\n");

}

// Driver code public static void Main(String[] args) { String s = "3+4i";

findModulo(s);

} } // This code contributed by sapnasingh4991

JavaScript

// JavaScript program to find the // Modulus of a Complex Number

// Function to find modulus // of a complex number function findModulo(s) { let l = s.length; let i, modulus = 0;

// Storing the index of '+'
if (s.indexOf('+')< l) {
    i = s.indexOf('+');
}
// Storing the index of '-'
else {
    i = s.indexOf('-');
}

// Finding the real part
// of the complex number
let real = s.substring(0, i);

// Finding the imaginary part
// of the complex number
let imaginary = s.substring(i + 1, l - 1);

let x = parseInt(real);
let y = parseInt(imaginary);

console.log(Math.sqrt(x*x + y*y));

}

// Driver code let s = "3+4i"; findModulo(s);

// The code is contributed by Gautam goel (gautamgoel962)

`

Time Complexity: O(1)
Auxiliary Space: O(1)

As constant extra space is used