Complex.md

1. Exercise: Complex

Complex models a complex number of the form z = a + ib where:

• a is a real number.
• b is a real number.

Implement Complex according to the following specification:

Method	Description	Usage	Exceptions
Complex()	Constructs a complex number with no real and no imaginary component.	Complex z; // z = 0 + 0i	None
Complex(double const& real)	Constructs a complex number with a real component but no imaginary component.	Complex z(42); // z = 42 + 0i	None
Complex(double const& real, double const& imaginary)	Constructs a complex number with a real and imaginary component.	Complex z(42, 75); // z = 42 + 75i	None
~Complex()	Destructor.		None
Complex conjugate()	Returns the conjugate of *this.	Complex z1(42, 75); // z1 = 42 + 75i Complex z2{z1.conjugate()}; // z2 = 42 - 75i	None
double modulus()	Returns the modulus of *this	Complex z(3, 4); // z = 3 + 4i double mod{z.modulus()}; // mod = 5	None
double argument()	Returns the argument of *this.	Complex z(3, 4); // z = 3 + 4i double arg{z.argument()}; // arg = 0.9273	None

In addition to the above specification, you must:

• Implement const-correctness for methods and member variables.
• Mark the default constructor as default or delete.
• Mark the destructor as default or delete.
• Use initialiser lists where required.
• Use delegating constructors where possible.
• Have correct access specifiers.

2. Exercise: Complex (Continued)

Take the Complex class from lab02-1 and extend it with the following specification:

Method	Description	Usage	Exceptions
Complex(Complex const& z)	Copy constructor.	Complex z1; Complex z2(z1);	None
Complex(Complex&& z)	Move constructor.	Complex z1; Complex z2(std::move(z1));	None
Complex& operator=(Complex const& z)	Copy assignment.	Complex z1; Complex z2; z2 = z1;	None
Complex& operator=(Complex&& z)	Move assignment.	Complex z1; Complex z2; z2 = std::move(z1);	None
static Complex make_conjugate(Complex const& z)	Returns the conjugate of z. Equivalent to z.conjugate().	Complex z1(42, 75); // z1 = 42 + 75i Complex z2{Complex::make_conjugate(z1)}; // z2 = 42 - 75i	None
friend Complex operator+(Complex const& lhs, Complex const& rhs)	Returns the addition of two complex numbers.	Complex z1(3, 4); // z1 = 3 + 4i Complex z2(4, 5); // z2 = 4 + 5i Complex z3{z1 + z2}; // z3 = 7 + 9i	None
friend Complex operator-(Complex const& lhs, Complex const& rhs)	Returns the subtraction of two complex numbers.	Complex z1(3, 4); // z1 = 3 + 4i Complex z2(4, 5); // z2 = 4 + 5i Complex z3{z1 - z2}; // z3 = -1 + -1i	None
friend Complex operator*(Complex const& lhs, Complex const& rhs)	Returns the multiplication of two complex numbers.	Complex z1(3, 4); // z1 = 3 + 4i Complex z2(4, 5); // z2 = 4 + 5i Complex z3{z1 * z2}; // z3 = -8 + 31i	None
friend bool operator==(Complex const& lhs, Complex const& rhs)	Returns true if real components are equal and imaginary components equal.	Complex z1(3, 4); // z1 = 3 + 4i Complex z2(4, 5); // z2 = 4 + 5i Complex z3(4, 5); // z3 = 4 + 5i bool t1{z1 == z2}; // false bool t2{z2 == z3}; // true	None
friend bool operator!=(Complex const& lhs, Complex const& rhs)	Returns false if real components are equal and imaginary components equal.	Complex z1(3, 4); // z1 = 3 + 4i Complex z2(4, 5); // z2 = 4 + 5i Complex z3(4, 5); // z3 = 4 + 5i bool t1{z1 != z2}; // true bool t2{z2 != z3}; // false	None
friend std::ostream& operator<<(std::ostream& os, Complex const& z)	Writes the complex number to the output in the format a+bi where a and b are the real and imaginary component respectively.	Complex z(3, 4); // z = 3 + 4i std::cout << z; // 3+4i	None

In addition to the above specification, you must:

• Implement const-correctness for methods and member variables.
• Mark appropriate constructors, assignments, and destructor as default or delete.
• Have correct access specifiers.
• Write more tests for the new methods.