Java Program to Add two Complex Numbers

A complex number is a number that consists of a real part and an imaginary part, and is written in the form a + bi, where a is the real part and b is the imaginary part. To add two complex numbers, simply add their real parts together and their imaginary parts together.

• The real and imaginary parts are added separately.
• A class can be used to represent and manipulate complex numbers in Java.

Illustration:

Input: z₁ = 4 + 5i, z₂ = 10 + 5i
Output: 14 + 10i

Input: z₁ = 3 + 2i, z₂ = 6 + 7i
Output: 9 + 9i

Formula to Add Two Complex Numbers

If we have two complex numbers:

• z₁ = a + bi
• z₂ = c + di

Then their addition is calculated as:

z₁ + z₂ = (a + c) + (b + d)i

Adding Two Complex Numbers

The addition of two complex numbers is done by adding the real parts and imaginary parts separately:

Example: Add Two Complex Numbers

class ComplexNumber {

    int real, imaginary;

    // Constructor
    ComplexNumber(int real, int imaginary) {
        this.real = real;
        this.imaginary = imaginary;
    }

    // Method to add two complex numbers
    ComplexNumber add(ComplexNumber other) {
        return new ComplexNumber(
            this.real + other.real,
            this.imaginary + other.imaginary
        );
    }

    // Method to display the complex number
    void display() {
        System.out.println(real + " + " + imaginary + "i");
    }

    public static void main(String[] args) {

        ComplexNumber c1 = new ComplexNumber(4, 5);
        ComplexNumber c2 = new ComplexNumber(10, 5);

        System.out.print("First Complex Number: ");
        c1.display();

        System.out.print("Second Complex Number: ");
        c2.display();

        ComplexNumber result = c1.add(c2);

        System.out.print("Sum: ");
        result.display();
    }
}

First Complex Number: 4 + 5i
Second Complex Number: 10 + 5i
Sum: 14 + 10i

Explanation: In this example, two complex numbers (4 + 5i and 10 + 5i) are created using the ComplexNumber class. The add() method adds their real parts and imaginary parts separately, creates a new complex number with the sum, and the display() method prints the result.