1. A complex number is a number in the form a bi, where a and b are real numbers

Question

1. A complex number is a number in the form a bi, where a and b are real numbers and i is sqrt(-1). The numbers a and b are known as the real part and imaginary part of the complex number, respectively. You can perform addition, subtraction, multiplication, and division for complex numbers using the following formulas a+bi + c + di = (a + c) + (b + d)i a+bi-(c + di) = (a-c)+(b-d)i (a bi) (c di) (ac bd) (bc+ ad)i (a bi)/(c di) (ac+ bd)/(c2 d2)(bc-ad)i/(c2+ d2) Design and implement a class named Complex for representing complex numbers and the methods add, subtract, multiply, and divide for performing complex number operations, and override the toString() method to return a string representation for a complex number The toString method returns (abi) as a string. If b is 0, it simply returns a. Implement three constructors: Complex(a, b), Complex(a), and Complex(). Complex() creates a Complex object for number 0 and Complex(a) creates a Complex object with 0 for b. You should also implement getRealPart() and getlmaginaryPart() methods for returning the real and imaginary part of the complex number, respectively. Write a test program that prompts the user to enter two complex numbers and displays the result of their addition, subtraction, multiplication, and division

Explanation / Answer

import java.io.*;

import java.util.*;

class Complex{

  

double real;

double imag;

  

Complex()

{

real=0;

imag=0;

}

Complex(double a)

{

real=a;

imag=0;

}

Complex(double a,double b)

{

real=a;

imag=b;

}

double getRealPart()

{

return real;

}

double getImaginaryPart()

{

return imag;

}

Complex addition(Complex c2)

{

Complex c3= new Complex();

c3.real=this.real+c2.real;

c3.imag=this.imag+c2.imag;

return c3;

}

Complex subtraction(Complex c2)

{

Complex c3= new Complex();

c3.real=this.real-c2.real;

c3.imag=this.imag-c2.imag;

return c3;

}

  

Complex multiplication( Complex a)

{

Complex n= new Complex();

n.real=this.real*a.real-imag*a.imag;

n.imag=this.real*a.imag+imag*a.real;

return n;

}

Complex division(Complex c2)

{

Complex n=new Complex();

double deno=Math.pow(c2.real,2)+Math.pow(c2.imag,2);

n.real=(this.real*c2.real+this.imag*c2.imag)/deno;

n.imag=(this.imag*c2.real-this.real*c2.imag)/deno;

return n;

}

void display()

{

System.out.println(" The number is "+real+" + "+imag+" i");

}

@Override

public String toString() {

return String.format(real +" + "+ imag+" i ");

}

}

public class HelloWorld{

public static void main(String []args){

  

Scanner input = new Scanner(System.in);

System.out.println(" Enter Real and Imaginery of First Complex Number");

double a = input.nextDouble();

double b = input.nextDouble();

  

System.out.println(" Enter Real and Imaginery of Second Complex Number");

double c = input.nextDouble();

double d = input.nextDouble();

  

Complex c1= new Complex(10,15);

Complex c2= new Complex(20,25);

Complex res=new Complex();

System.out.println(" Addition ");

res= c1.addition(c2);

res.display();

System.out.println(" In String "+res.toString());

System.out.println(" Subtraction ");

res= c1.subtraction(c2);

res.display();

System.out.println(" In String "+res.toString());

System.out.println(" Multiplication ");

res=c1.multiplication(c2);

res.display();

System.out.println(" In String "+res.toString());

System.out.println(" Division ");

res=c1.division(c2);

res.display();

System.out.println(" In String "+res.toString());

}

}

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