Part 1: Applications to Mathematics using Classes and Objects Question #1-Complex Numbers (40pts) Write a class called Complex for performing arithmetic with complex numbers. Complex numbers have the following forms: realPart+imaginaryPart* I where i--1 Write a program to test your class. Use floating-point variables to represent the private data of the class. Provide a constructor that enables an object of this class to be initialized when it is declared. Provide a no-argument constructor with defaults values in case no initializers are provided. Provide the following public methods that perform the following operations: a) Add two complex numbers (the real parts are added together, and the imaginary parts are added together) b) Subtract two complex numbers (the rcal part of the right opcrand is subtracted from the real part of the left operand, and the imaginary part of the right operand is subtracted from the imaginary part of the left operand) c) Print Complex numbers in the form (realPart, imaginary Part) Question #2- Rational Numbers (40pts) Create a class called Rational for performing arithmetic with fractions. Write a program to test your class. Use integer variables to represent the private instance variable of the class-the numerator and the denominator. Provide a constructor that enables an object of this class to be initialized when it is declared. The Constructor should store the fraction in reduced form (the fraction 2/4 is equivalent to y and would be stored as the object 1 in the numerator and 2 in the denominator). Provide a no-argument constructor with defaults values in case no initializers are provided. Provide public methods that perform cach of the following operations: a) Add two Rational numbers b) Subtract two rational numbers part of the left operand, and the imaginary part of the right operand is subtracted from the imaginary part of the left operand) c) Print Complex numbers in the form (realPart, imaginary Part) Question #2- Rational Numbers (40pts) Create a class called Rational for performing arithmetic with fractions. Write a program to test your class. Use integer variables to represent the private instance variable of the class-the numcrator and the denominator. Provide a constructor that enables an object of this class to be initialized when it is declared. The Constructor should store the fraction in reduced form (the fraction 2/4 is equivalent to y and would be stored as the object 1 in the numerator and 2 in the denominator). Provide a no-argument constructor with defaults values in case no initializers are provided. Provide public mcthods that perform cach of the following operations: a) Add two Rational numbers b) Subtract two rational numbers c) Multiply two rational numbers d) Divide two rational numbers c) Retum a String representing of a rational number in the form a/b (where a is the numerator and b is the denominator)
