Chapter 8, Problem 3PP

Define a class for complex numbers. A complex number is a number of the form

$a+b*i$

where for our purposes, a and b are numbers of type double, and i is a number that represents the quantity $\sqrt{-1}.$ Represent a complex number as two values of type double. Name the member variables real and imaginary. (The variable for the number that is multiplied by i is the one called imaginary.) Call the class Complex. Include a constructor with two parameters of type double that can be used to set the member variables of an object to any values. Include a constructor that has only a single parameter of type double; call this parameter realPart and define the constructor so that the object will be initialized to realPart $+0*i.$ Include a default constructor that initializes an object to o (that is, to $0+0*i).$ Overload all the following operators so that they correctly apply to the type $==,+,-,*,>>,$ and $<<.$ You should also write a test program to test your class. Hints: To add or subtract two complex numbers, add or subtract the two member variables of type double. The product of two complex numbers is given by the following formula:

$\left(a+b*i\right)*\left(c+d*i\right)==\left(a*c-b*d\right)+\left(a*d+b*c\right)*i$

In the interface file, you should define a constant i as follows:

const Complex $i\left(0,1\right);$

This defined constant i will be the same as the i discussed above.