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Showing content from https://www.geeksforgeeks.org/java/java-program-to-add-two-complex-numbers/ below:

Java Program to Add two Complex Numbers

Last Updated : 13 Jul, 2022

Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra. The standard format for complex numbers is a + bi, with the real number first and the imaginary number last.

General form for any complex number is:

a+ib

Where "a" is real number and "b" is Imaginary number.

Construction of Complex number

For creating a complex numbers, we will pass imaginary numbers and real numbers as parameters for constructors.

Java


 // Java program to construct the complex number

class ComplexNumber {

    // variables to hold real and imaginary part of complex
    // number
    int real, image;

    // Constructor which will be used while creating complex
    // number
    public ComplexNumber(int r, int i)
    {
        this.real = r;
        this.image = i;
    }

    // function to print real number
    public void showC()
    {
        System.out.println(this.real + " +i " + this.image);
    }

    // we will implement  this function for addition
    public complex add(ComplexNumber, ComplexNumber);
}

Time Complexity: O(1)

Auxiliary Space: O(1)

Add function

Basically, addition of two complex numbers is done by adding real part of the first complex number with real part of the second complex number.
And adding imaginary part of the first complex number with the second which results into the third complex number.
So that means our add() will return another complex number.

Ex. addition of two complex numbers

(a1) + (b1)i -----(1)

(a2)+ (b2)i -----(2)

adding (1) and (2) will look like

(a1+a2) + (b1+b2)i

Function Definition:

ComplexNumber add(ComplexNumber n1, ComplexNumber n2){
    
  ComplexNumber res = new ComplexNumber(0,0); //creating blank complex number 
  
  // adding real parts of both complex numbers
  res.real = n1.real + n2.real;
  
  // adding imaginary parts
  res.image = n1.image + n2.image;
  
  // returning result
  return res;

}

Code:

Java


 // Java program to add two complex numbers

class ComplexNumber {

    // variables to hold real and imaginary part of complex
    // number
    int real, image;

    // Constructor which will be used while creating complex
    // number
    public ComplexNumber(int r, int i)
    {
        this.real = r;
        this.image = i;
    }

    // function to print real number
    public void showC()
    {
        System.out.print(this.real + " +i" + this.image);
    }

    // function for addition
    public static ComplexNumber add(ComplexNumber n1,
                                    ComplexNumber n2)
    {

        // creating blank complex number
        // to store result
        ComplexNumber res = new ComplexNumber(0, 0);

        // adding real parts of both complex numbers
        res.real = n1.real + n2.real;

        // adding imaginary parts
        res.image = n1.image + n2.image;

        // returning result
        return res;
    }

    public static void main(String arg[])
    {

        // creating two complex numbers
        ComplexNumber c1 = new ComplexNumber(4, 5);
        ComplexNumber c2 = new ComplexNumber(10, 5);

        // printing complex numbers
          System.out.print("first Complex number: ");
        c1.showC();
        
        System.out.print("\nSecond Complex number: ");
        c2.showC();

        // calling add() to perform addition
        ComplexNumber res = add(c1, c2);

        // displaying addition
        System.out.println("\nAddition is :");
        res.showC();
    }
}

Output

first Complex number: 4 +i5
Second Complex number: 10 +i5
Addition is :
14 +i10

Time Complexity: O(1)

Auxiliary Space: O(1)

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