Question

JAVA Programming

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)/(c^2 +d^2) + (bc-ad)i/(c^2 +d^2)

You can also obtain the absolute value for a complex number using the following formula:

| a + bi | = sqrt(a^2 + b^2)

(A complex number can be interpreted as a point on a plane by identifying the (a, b) values as the coordinates of the point. The absolute value of the complex number corresponds to the distance of the point to the origin, as shown in Figure 13.10.)

Design a class named Complex for representing complex numbers and the methods add, subtract, multiply, divide, and abs for performing complex number operations, and override the toString method for returning a string representation for a complex number. The toString method returns (a + bi) as a string. If b is 0, it simply returns a. Your Complex class should also implement Cloneable and Comparable. Compare two complex numbers using their absolute values.

Provide 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. Also provide the getRealPart() and getImaginaryPart() methods for returning the real and imaginary part of the complex number, respectively.

Use the code at

https://liveexample.pearsoncmg.com/test/Exercise13_17.txt

to test your implementation.

Sample Run

Enter the first complex number: 3.5 5.5

Enter the second complex number: -3.5 1

(3.5 + 5.5i) + (-3.5 + 1.0i) = 0.0 + 6.5i

(3.5 + 5.5i) - (-3.5 + 1.0i) = 7.0 + 4.5i

(3.5 + 5.5i) * (-3.5 + 1.0i) = -17.75 -15.75i

(3.5 + 5.5i) / (-3.5 + 1.0i) = -0.5094339622641509 -1.7169811320754718i

|3.5 + 5.5i| = 6.519202405202649

false

3.5

5.5

[-3.5 + 1.0i, 4.0 + -0.5i, 3.5 + 5.5i, 3.5 + 5.5i]

The Output must be similar to the Sample Run

The Class Name MUST be Exercise13_17

If you get a logical or runtime error, please refer https://liveexample.pearsoncmg.com/faq.html.

Answer 1

Please find my implementation.

public class ComplexNumber {

   private double real;

   private double imag;

   // default constructor

   public ComplexNumber() {

       real = imag = 0;

   }

   // parameterized constructor

   public ComplexNumber(double r, double i) {

       real = r;

       imag = i;

   }

   // parameterized constructor

   public ComplexNumber(double a) {

       real = a;

       imag = 0;

   }

   // copy constructor

   public ComplexNumber(ComplexNumber other){

       real = other.real;

       imag= other.imag;

   }

   public double getReal() {

       return real;

   }

   public double getImaginary() {

       return imag;

   }

   // toString method

   public String toString() {

       return "("+String.format("%.2f", real)+" + "+String.format("%.2f", imag)+"i)";

   }

   // function to add

   public ComplexNumber add(ComplexNumber other){

       ComplexNumber sum = new ComplexNumber();

       sum.real = real + other.real;

       sum.imag = imag + other.imag;

       return sum;

   }

   // function to suntract

   public ComplexNumber subtract(ComplexNumber other){

       ComplexNumber sub = new ComplexNumber();

       sub.real = real - other.real;

       sub.imag = imag - other.imag;

       return sub;

   }

   // function to multiply

   public ComplexNumber multiplyBy(ComplexNumber other){

       ComplexNumber mul = new ComplexNumber();

       mul.real = real*other.real + imag*other.imag;

       mul.imag = imag*other.real + other.imag*real;

       return mul;

   }

   // function to divide

   public ComplexNumber divideBy(ComplexNumber other){

       if(other.real == 0 && other.imag == 0)

           throw new IllegalArgumentException("Both ral and imaginary part of denominator can not be zero");

       ComplexNumber divide = new ComplexNumber();

       divide.real=((real*other.real)+(imag*other.imag))/((other.real*other.real)+(other.imag*other.imag));

       divide.imag=((imag*other.real)-(real*other.imag))/((other.real*other.real)+(other.imag*other.imag));

       return divide;

   }

  

   public double abs(){

       return Math.sqrt(real*real + imag*imag);

   }

   public boolean isRealPart(){

       return imag ==0;

   }

   public boolean isImaginaryPart(){

       return real == 0;

   }

}

###########

import java.util.Scanner;

public class ComplexNumberTesting {

  

   public static void main(String[] args) {

      

       Scanner sc = new Scanner(System.in);

      

       System.out.print("Enter the first complex number: ");

       double r = sc.nextDouble();

       double img = sc.nextDouble();

      

       ComplexNumber c1 =new ComplexNumber(r,img);

      

       System.out.print("Enter the second complex number: ");

       r = sc.nextDouble();

       img = sc.nextDouble();

      

       sc.close();

      

       ComplexNumber c2 = new ComplexNumber(r,img);

      

       System.out.println("C1: "+c1);

       System.out.println("C2: "+c2);

      

       ComplexNumber sum = c1.add(c2);

       System.out.println(c1+"+"+c2+" = " +sum);

      

       ComplexNumber sub = c1.subtract(c2);

       System.out.println(c1+"-"+c2+" = " +sub);

      

       ComplexNumber mul = c1.multiplyBy(c2);

       System.out.println(c1+"*"+c2+" = " +mul);

      

       ComplexNumber divide = c1.divideBy(c2);

       System.out.println(c1+"/"+c2+" = " +divide);

      

       System.out.println("|"+c1+"| = "+c1.abs());

   }

}

/*

Sample Output:

Enter the first complex number: 3.5 5.5

Enter the second complex number: -3.5 1

C1: (3.50 + 5.50i)

C2: (-3.50 + 1.00i)

(3.50 + 5.50i)+(-3.50 + 1.00i) = (0.00 + 6.50i)

(3.50 + 5.50i)-(-3.50 + 1.00i) = (7.00 + 4.50i)

(3.50 + 5.50i)*(-3.50 + 1.00i) = (-6.75 + -15.75i)

(3.50 + 5.50i)/(-3.50 + 1.00i) = (-0.51 + -1.72i)

|(3.50 + 5.50i)| = 6.519202405202649

*/