Java Program to Add two Complex Numbers

Complex numbers consist of two components - a real number and an imaginary number, which are distinct from each other. These numbers are widely used in mathematics, particularly in algebra. The standard format for a complex number is a + bi, where "a" represents the real number component and "b" represents the imaginary number component.

The general representation of a complex number follows a specific format, which includes both a real part and an imaginary part.

a+ib
where "a" is the real number component and "b" is the imaginary number component.

Example

Suppose we have two complex numbers:
(3 + 2i) --- (1)
(2 + 5i) --- (2)
To add these two complex numbers, we will add the real and imaginary parts separately:
Real part = 3 + 2 = 5
Imaginary part = 2 + 5 = 7
Therefore, the sum of the two complex numbers is:
(5 + 7i)

Algorithm:

Define a class named "ComplexNumber" with variables "real" and "imag" to hold the real and imaginary parts of the complex number.
To initialise the real and imaginary components of the complex number, create a constructor for the class.
Define a method named "showC" to print the complex number as (a + bi).
Define a static method named "add" to add two complex numbers. The method takes two ComplexNumber objects as parameters and returns a ComplexNumber object.
Create a new ComplexNumber object to store the addition result in the add method.
Add the real parts of the two complex numbers and assign the result to the real part of the new ComplexNumber object. Similarly, add the imaginary parts of the two complex numbers and assign the result to the imaginary part of the new ComplexNumber object.

Implementation:

Filename: ComplexNumber.java

class ComplexNumber {

    // real and imaginary components of the complex integer are stored in variables.
    int real, imag;

    // The constructor is a method that is used to create instances of complex numbers with specific values assigned to the real and imaginary parts.
    public ComplexNumber(int r, int i) {
        this.real = r;
        this.imag = i;
    }

    //Display the complex number in the form of (a + bi)
    public void showC() {
        System.out.print("(" + this.real + " + " + this.imag + "i" + ")");
    }

    // Addition of two complex numbers
    public static ComplexNumber add(ComplexNumber n1, ComplexNumber n2) {

        // Creating a new variable to store the result
        ComplexNumber res = new ComplexNumber(0, 0);

        // To perform addition of two complex numbers, the real parts of each number are added together.
        res.real = n1.real + n2.real;

        // Adding imaginary parts of both complex numbers
        res.imag = n1.imag + n2.imag;

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

Output:

First Complex number: (4 + 5i)
Second Complex number: (10 + 5i)
Addition is :
(14 + 10i)

Complexity Analysis:

The time complexity of the add method in the ComplexNumber class is O(1), as it performs a constant number of operations (adding the real and imaginary parts of the complex numbers). The time complexity of the showC method is also O(1), as it performs a constant number of operations (printing the real and imaginary parts in a specific format). The time complexity of the main method is also O(1), as it creates two complex numbers, calls the add method to perform the addition, and then calls the showC method to display the result.

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