A complex number is a number in the form a+bi, where a and b are real numbers and i is √(-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 (addition)a + bi − (c + di) = (a−c) + (b−d)i (subtraction)(a + bi) * (c + di) = (ac−bd) + (bc+ad)i (multiplication)(a + bi) / (c + di) = (ac+bd) / (c2+d2) + (bc−ad)i / (c2+d2) (division) You can obtain the Absolute Value for a complex number using the following formula:|a + bi| = √(a2 + b2) 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 the example below. (1) Design a class named Complex for representing complex numbersInclude methods add, subtract, multiply, divide, and abs for performing complex-number operationsOverride 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 0Complex(a) creates a Complex object with 0 for b.Also provide the getRealPart() and get imaginary part() methods for returning the real part and the imaginary part of the complex number, respectively. (2) Draw the UML class diagram and implement the class. (3) Write a Test programPrompt the user to enter two complex numbersDisplays the result of their addition, subtraction, multiplication, division, and absolute value.A sample run is shown below: 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) = –0.5094 + –1.7i|(3.5 + 5.5i)| = 6.519202405202649

import java.lang.Math; //Complex class.public class Complex implements Cloneable,Comparable<Complex>{ //private members. private double real; private double imaginary; //Tostring method. @Override public String toString() { String result; if (imaginary==0) result=String.valueOf(real); else result= "("+String.valueOf(real)+ "+ "+String.valueOf(imaginary)+ "i" +")"; return result; } //Constructors: //Default constructor. //Assigning the variables to zero. Complex() { real=0; imaginary=0; } //Parameterized constructor. //one parameter Complex(double a){ real=a; imaginary=0; } //Parameterized constructor. //Two parameters. Complex(double a, double b){ real=a; imaginary=b; } //Function to return real part. double getRealPart(){ return real; } //Function to return imaginary part. double getimaginarypart(){ return imaginary; } //Adding two complex numbers. void add(double a, double b){ double resultReal = a+real; double resultImag = b+imaginary; System.out.println(String.valueOf(resultReal)+ "+ "+String.valueOf(resultImag)+ "i"); } //Subtraction of two complex numbers. void subtract(double a, double b){ double resultReal = real-a; double resultImag = imaginary-b; System.out.println(String.valueOf(resultReal)+ "+ "+String.valueOf(resultImag)+ "i"); } //Multiply two complex numbers. void multiply(double a, double b){ double resultReal = (real*a)-(imaginary*b) ; double resultImag = (imaginary*a+real*b); System.out.println(String.valueOf(resultReal)+ "+ "+String.valueOf(resultImag)+ "i"); } //Divide two complex numbers. void divide(double a, double b){ double resultReal = (real*a+imaginary*b) / (a*a+b*b) ; double resultImag = (imaginary*a-real*b) / (a*a+b*b) ; System.out.println(String.valueOf(resultReal)+ "+ "+String.valueOf(resultImag)+ "i"); } //Getting absolute value. double abs(){ double result= Math.sqrt(real*real+imaginary*imaginary); return result; } // Overriding clone() method // by simply calling Object class // clone() method. @Override protected Object clone() throws CloneNotSupportedException{ return super.clone(); } public int compareTo(Complex c){ double first=abs(); double second = c.abs(); if (first==second) return 1; else return 0; } };import java.util.*; public class Test{ public static void main(String[] args) { // scanner input Scanner sc= new Scanner(System.in); //Enter the first number. System.out.println("Enter the first complex number"); double a = sc.nextDouble(); double b = sc.nextDouble(); //Enter the second number. System.out.println("Enter the second complex number"); double c = sc.nextDouble(); double d = sc.nextDouble(); Complex first = new Complex(a,b); Complex second = new Complex(c,d); //Addition System.out.print(first.toString()+ " + "+second.toString()+ " = "); first.add(c,d); //Subtraction. System.out.print(first.toString()+ " - "+second.toString()+ " = "); first.subtract(c,d); //Multiplication System.out.print(first.toString()+ " * "+second.toString()+ " = "); first.multiply(c,d); //Division System.out.print(first.toString()+ " / "+second.toString()+ " = "); first.divide(c,d); //Absolute value. System.out.print("(|"+first.toString()+"|) ="); double res=first.abs(); System.out.println(res); }}

Answered: complex number

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Question

A complex number is a number in the form a+bi, where a and b are real numbers and i is √(-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 (addition)

a + bi − (c + di) = (a−c) + (b−d)i (subtraction)

(a + bi) * (c + di) = (ac−bd) + (bc+ad)i (multiplication)

(a + bi) / (c + di) = (ac+bd) / (c²+d²) + (bc−ad)i / (c²+d²) (division)

You can obtain the Absolute Value for a complex number using the following formula:

|a + bi| = √(a² + b²)

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 the example below.

(1) Design a class named Complex for representing complex numbers

Include methods add, subtract, multiply, divide, and abs for performing complex-number operations
Override 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
Complex(a) creates a Complex object with 0 for b.

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

(2) Draw the UML class diagram and implement the class.

(3) Write a Test program

Prompt the user to enter two complex numbers
Displays the result of their addition, subtraction, multiplication, division, and absolute value.

A sample run is shown below:

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) = –0.5094 + –1.7i

|(3.5 + 5.5i)| = 6.519202405202649

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.