Question

Use double 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. The constructor should contain default values in case no initializers are provided. Provide public member functions that perform the following tasks: a. Adding two complex numbers: The real parts are added together and the imaginary parts are added together. b. Subtracting two complex numbers: The real part of the right operand 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. Printing complex numbers in the form (a, b), where a is the real part and b is the imaginary part.

Short answer

Use the `ComplexNumber` class with real and imaginary doubles, constructors, and functions to add, subtract, and print.

Step-by-step solution

Define the ComplexNumber Class

Create a class named `ComplexNumber` with private data members to represent the real and imaginary parts of a complex number. Use double variables `real` and `imaginary` to store these values.

Implement the Constructor

Define a constructor for the `ComplexNumber` class that takes two arguments. Set the private members `real` and `imaginary` to these arguments. Provide default values such as 0.0 for both arguments in case no initializers are provided.

Create the Add Function

Create a public member function named `add` that takes another `ComplexNumber` object as a parameter. Inside this function, add the real part of the parameter to the real part of the current object, and the imaginary part of the parameter to the imaginary part of the current object. Return a new `ComplexNumber` object with these summed parts.

Create the Subtract Function

Create a public member function named `subtract` that takes another `ComplexNumber` object as a parameter. Subtract the real part of the parameter from the real part of the current object, and subtract the imaginary part of the parameter from the imaginary part of the current object. Return a new `ComplexNumber` object with these differences.

Implement the Print Function

Create a public member function named `print` that prints the complex number in the format (a, b), where `a` is the real part and `b` is the imaginary part. Use standard output to achieve this.

Testing the Functions

Create a few `ComplexNumber` objects and test the `add`, `subtract`, and `print` functions to ensure they perform correctly. Use the default constructor values and specified values to verify correct behavior.

Key concepts

Complex Numbers

Complex numbers are numbers that comprise a real and an imaginary part. Typically, a complex number is represented in the form \(a + bi\), where \(a\) is the real part and \(b\) represents the imaginary part. The imaginary part is a multiple of the imaginary unit \(i\), which is defined as \(\sqrt{-1}\).

Students often encounter complex numbers in mathematics, especially in algebra and engineering. They are vital for describing phenomena such as electrical circuits and fluid dynamics. Complex numbers have mathematical operations such as addition and subtraction, just like real numbers.

The key difference is that when adding or subtracting complex numbers, you handle the real parts and imaginary parts separately:

• For addition, if you have two complex numbers \((a+bi)\) and \((c+di)\), their sum is \((a+c) + (b+d)i\).
• For subtraction, the difference of two complex numbers \((a+bi)\) and \((c+di)\) is \((a-c) + (b-d)i\).

This separation of real and imaginary components must be factored into any class design that aims to work with complex numbers.

Constructor Overloading

Constructor overloading is a concept in C++ that allows a class to have more than one constructor with different parameters. This gives flexibility to use different ways to initialize objects depending on the given situation.

For a class that deals with complex numbers, constructor overloading enables the creation of objects with initial values or default values without any initialization. In C++, this is achieved by defining multiple constructors with different parameter lists in the class.

For instance, consider the `ComplexNumber` class from our exercise:

• You can have one constructor that accepts two parameters (usually for the real and imaginary parts) to initialize the object with specific values.
• You can also define a default constructor that sets default values such as 0.0 for both the real and imaginary parts if no arguments are provided during initialization.

This makes your code more robust and allows more freedom to the user of the class, providing them options based on their needs.

Member Functions

Member functions in C++ are functions that operate on objects of a class. They are essential for interacting with the class's private data members, enabling the encapsulation of data.

In the context of the `ComplexNumber` class, member functions like `add`, `subtract`, and `print` perform specific tasks on complex numbers:

• The `add` function computes the sum of the current complex number object with another object. It separately sums the real and imaginary parts and returns a new `ComplexNumber` object.
• Similarly, the `subtract` function calculates the difference, which involves subtracting real parts and imaginary parts individually and returns the result as a new `ComplexNumber`.
• The `print` function outputs the complex number's real and imaginary parts in a readable format (\((a, b)\)).

These member functions make the class functional and allow users to perform operations seamlessly on complex numbers, thus encouraging modular and object-oriented programming.

Object Initialization

Object initialization in C++ refers to the assignment of an initial state to an instance of a class. It is a fundamental step in object-oriented programming as initialized objects are ready for use in the program.

In our exercise context, initializing a `ComplexNumber` object is key to ensuring that the real and imaginary parts have valid starting values. Without proper initialization, these parts could contain garbage values, leading to incorrect computations.

• Using constructors, especially with default values, aids object initialization. When a `ComplexNumber` object is declared, the constructor assigns user-provided or default values to the real and imaginary parts.

This step is crucial as it sets a reliable initial state for the object, facilitating accurate arithmetic operations later on. Proper initialization also adheres to good software design practices, enforcing data correctness and predictability in how the class behaves.