*13.17 (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 2 - 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)

 

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

 

I a  + bi I   =  2a2  + 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 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 toString method for returning a string repre- sentation 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 the Cloneable interface.

Provide three constructors Complex(a, b), Complex(a), and Complex(). Complex() creates a Complex object for number 0 and  Complex(a) cre- ates 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.

Write a test program that prompts the user to enter two complex numbers and displays the result of their addition, subtraction, multiplication, division, and abso- lute value. Here is a sample run: