Question

ASAP

(Math: The Complex class)

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 13.10b.)

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 toStringmethod 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 andComparable. 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_17Test.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]

Class Name: Exercise13_17

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

Answer 1

public class Complex implements Cloneable, Comparable<Complex> {
  
   private double RealPart;
   private double ImaginaryPart;
  

   public Complex(double realPart, double imaginaryPart) {
       RealPart = realPart;
       ImaginaryPart = imaginaryPart;
   }
  
   public Complex() {
       RealPart = 0;
       ImaginaryPart = 0;
   }
   public Complex(double realPart) {
       super();
       RealPart = realPart;
       ImaginaryPart = 0;
   }

   public double getRealPart() {
       return RealPart;
   }

   public double getImaginaryPart() {
       return ImaginaryPart;
   }
  
   public Complex add(Complex num) {
       return new Complex(this.getRealPart()+num.getRealPart(),this.ImaginaryPart+num.ImaginaryPart);
   }

   public Complex subtract(Complex num) {
       return new Complex(this.getRealPart()-num.getRealPart(),this.ImaginaryPart-num.ImaginaryPart);
   }
  
   public Complex multiply(Complex num) {
       double a = this.getRealPart();
       double b = this.getImaginaryPart();
       double c = num.getRealPart();
       double d = num.getImaginaryPart();
       return new Complex(a*c-b*d, b*c+a*d);
   }
  
   public Complex divide(Complex num) {
       double a = this.getRealPart();
       double b = this.getImaginaryPart();
       double c = num.getRealPart();
       double d = num.getImaginaryPart();
       return new Complex((a*c+b*d)/(c*c+d*d), (b*c-a*d)/(c*c+d*d));
   }
  
   public double abs() {
       return Math.sqrt(this.RealPart*this.RealPart+this.ImaginaryPart*this.ImaginaryPart);
   }

   @Override
   public int compareTo(Complex num) {
       if (this.abs()>num.abs())
           return 1;
       if (this.abs()<num.abs())
           return -1;
       return 0;
   }
  
   @Override
   public Object clone(){
       try {
           return super.clone();
       } catch (CloneNotSupportedException e) {
           e.printStackTrace();
       }
       return null;
       }
  
   @Override
   public String toString() {
       if(this.ImaginaryPart==0)
           return this.RealPart+"";
       else
           if(this.ImaginaryPart<0)
               return this.RealPart+" "+this.ImaginaryPart+"i";
           else
               return this.RealPart+" + "+this.ImaginaryPart+"i";
      
   }

}