Include the exact class name provided.

Language : JAVA

(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 13.10.)

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]

Class Name:

Exercise13_17

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