Implementing Complex Numbers with Class

Java has a number of built-in types such as int, char, boolean, float, and double, among others. Scientists and engineers often like to work with complex numbers, but complex numbers are not a built-in type in Java. Therefore, your task is to implement a complex number class. The class should be implemented in a file named Complex.java.

Recall that a complex number is of the form a + bi where a and b are real numbers and i is an imaginary number. Addition of two complex numbers is defined by (a + bi) + (c + di) = (a+c) + (b+d)i. Similarly, to multiply two complex numbers, we simply compute (a + bi) * (c + di) = ac + adi + bci + bdi² = (ac - bd) + (ad + bc) i since i² is -1 by definition.

In your implementation, the numbers a and b in the complex number a + bi should be represented by doubles. Below are the public methods (functions) that your Complex class should contain. Be sure to use exactly these names and the specified kinds of arguments and return values. You may use any additional private methods that you like in order to build your public methods.

• The class should have a constructor that takes two double arguments and sets the real and imaginary components of the complex number to these values.
• The class should have a second constructor that takes no arguments and simply sets the real and imaginary components of the complex number to both be 0.0.
• The class should have a method called equals that takes a Complex argument and determines if the two Complex numbers (this one and the argument) are equal. The method returns a boolean which is true if the numbers are equal and false otherwise.
• The class should have a method called add that takes a Complex argument and returns the sum of this Complex number and the argument. Thus, the return value is a Complex number itself and neither of the summands has their values changed in any way.
• The class should have a method called multiply that takes a Complex argument and returns the product of this Complex number and the argument. Thus the return value is a Complex number itself and neither of the multiplicands has their values changed in any way.
• The class should have a toString() method that converts complex numbers into strings for the sake of printing.

As always, write a program to test your Complex class.