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Modulus of a Complex Number
• Last Updated : 15 Apr, 2020

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

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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

2. Find the square of x and y separately.
Square of Real part = x2
Square of Imaginary part = y2

3. Find the sum of the computed squares.
Sum = Square of Real part
+ Square of Imaginary part
= x2 + y2

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

Below is the implementation of the above approach:

C++

 // C++ program to find the// Modulus of a Complex Number  #include using namespace std;  // Function to find modulus// of a complex numbervoid 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 codeint main(){    string s = "3+4i";      findModulo(s);      return 0;}

Java

 // Java program to find the// Modulus of a Complex Numberimport java.util.*;  class GFG{   // Function to find modulus// of a complex numberstatic 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 codepublic 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 Numberfrom math import sqrt  # Function to find modulus# of a complex numberdef 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 codeif __name__ == '__main__':    s = "3+4i"      findModulo(s)  # This code is contributed by Surendra_Gangwar

C#

 // C# program to find the// Modulus of a Complex Numberusing System;  public class GFG{    // Function to find modulus// of a complex numberstatic 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 codepublic static void Main(String[] args){    String s = "3+4i";        findModulo(s);}}// This code contributed by sapnasingh4991
Output:
5


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