Chapter 11, 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. 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. Also 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. Also include a default constructor that initializes an object to 0 (that is, to 0+0*i). Overload all of the following operators so that they correctly apply to the type Complex: ==, +, −, *, >>, and <<. You should write a test program to test your class.

(Hints: To add or subtract two complex numbers, you add or subtract the two member variables of type double. The product of two complex numbers is given by the following formula:

(a + b*i)*(c + d*i) == (a*c – b*d) + (a*d + b*c)*i

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 earlier.

delete p;