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 . Represent a complex number as two values of type double. Name the member variables real and imaginary. (The vari- able 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 0 (that is, to 0 + 0* i). Overload all the following operators so that they correctly apply to the type Complex : ==, +, -, *, >>, 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:

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

const Complex i(0, 1);

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