Using the Rat Class as a guideline, complete the essentials for a complex number class.

A complex number can be represented as a+bi.

When adding, simple add the two parts separately

e.g. (4+5i) + (7-3i) = 11 + 2i

When multiplying, the terms need to "cross": just as you would do with (a+b) * (c+d)

e.g. (4+5i) * (7-3i) = 4*7 + 5*7i - 3*4i -3*5ii = 28 + (35-12)i - 15(-1) = (28+15) + 23i = 43 + 23i

Normal: A complex number can have a real part and the imaginary part. Use double to implement them.

Extra Credit: Use Rat instead of double.

Note: If you want to implement Extra Credit on a separate file, you can attach a link.

#include

using namespace std;

class Complex {

private:

double r;

double i;

public:

// constructors

// default constructor

Complex() {

r = 0;

i = 0;

}

Complex(double r1) {

//fill this in

}

Complex(double r1, double i1) {

//fill this in

}

// setters and getters (these should be easy)

int getR() {

}

int getI() {

}

void setR(double r1) {

}

void setI(double i1) {

}

// arithmetic operators

Complex operator+(Complex c) {

}

Complex operator-(Complex c) {

}

Complex operator*(Complex c) {

}

Complex operator/(Complex c) {

}

//We only need to output for this one

friend ostream &operator<<(ostream &os, Complex c);

}; // end of Complex Class

ostream &operator<<(ostream &os, Complex c) {

//fill this in as well

//if a complex number only has the real part, only print the real part

//i.e. Do not print 4+0i

}

int main() {

Complex c1, c2(1), c3(1,1);

cout << c1 << endl;

cout << c2 << endl;

cout << c3 << endl;

c1 = c2 + c3;

cout << c1 << endl;

c3 = c1 * c2;

cout << c3 << endl;

c3 = c3 / c2;

cout << c3 << endl;

c2 = c2 - c2;

cout << c2 << endl;

//feel free to add your own tests below here.

return 0;

}