Problem $2$

Implement class Complex

A complex number is a number of the form $a+bi,$ where a and $b$ are real numbers and $i$ is

$\sqrt[\phantom{2}]{-1}.$ 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 formula:

$a+bi+c+di=(a+c)+(b+d)i$

$a+bi-(c+di)=(a-c)+(b-d)i$

$(a+bi)**(c+di)=(ac-bd)+(bc+ad)i$

$\frac{a+bi}{c+di}=\frac{ac+bd}{c^2+d^2}+(bc-ad)\frac{i}{c^2+d^2}$

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

$|a+bi|=\sqrt[\phantom{2}]{a^2+b^2}$

Design a class named Complex for representing complex numbers and the methods add,

subtract, multiply, divide, abs for performing complex$-$number operations, and override

toString, equals, compare To and clone methods.

Your Complex class should implement the Cloneable and Comparable interfaces.

Provide three constructors Complex $($a$,$ b$),$ Complex$($a$),$ and Complex$().$ Complex$()$ creates a

Setters and getters. Also provide the getRealPart$()$ and getImaginaryPart$()$ methods for

returning the real and imaginary part of the complex number, respectively.

Test your class Complex with the code provided in class MP$3$ in page $3.$

You should produce the same outputs with the sample outputs given.