Complex Number Class

//
//  main.cpp
//  complex
//
//  Created by Mark Brautigam on 11/21/16.
//  Copyright © 2016 Mark Brautigam. All rights reserved.
//

#include <iostream>
#include <cmath>
#include <assert.h>
using namespace std;

class Complex {
private:
    double real, imag; // rectangular coordinates
    double mag, theta; // polar coordinates
    bool cartesian, polar; // which set is valid?
    
    void calculateCartesian();
    void calculatePolar();
    
public:
    Complex();
    Complex(double r, double i);
    double getReal();
    double getImag();
    double getMag();
    double getTheta();
    void printCartesian();
    void printPolar();
    void setPolar (double m, double t);
};

void Complex::setPolar (double m, double t) {
    mag = m;
    theta = t;
    cartesian = false;
    polar = true;
}


void Complex::printCartesian() {
    cout << getReal() << " + " << getImag() << "i\n";
}

void Complex::printPolar() {
    cout << getMag() << " e^ " << getTheta() << "i\n";
}

void Complex::calculateCartesian() {
    assert(polar);
    real = mag * cos (theta);
    imag = mag * sin (theta);
    cartesian = true;
}

// not in textbook
void Complex::calculatePolar() {
    assert (cartesian);
    mag = sqrt (real * real + imag * imag);
    theta = atan ( imag / real );
    polar = true;
}

Complex::Complex () {
    cartesian = false;
    polar = false;
}

Complex::Complex (double r, double i) {
    real = r;
    imag = i;
    cartesian = true;
    polar = false;
}

double Complex::getReal() {
    if (cartesian == false)
        calculateCartesian();
    return real;
}

// not in textbook
double Complex::getImag() {
    if (cartesian == false)
        calculateCartesian();
    return imag;
}

// not in textbook
double Complex::getMag() {
    if (polar == false)
        calculatePolar();
    return mag;
}

// not in textbook
double Complex::getTheta() {
    if (polar == false)
        calculatePolar();
    return theta;
}

Complex add (Complex a, Complex b) {
    double real = a.getReal() + b.getReal();
    double imag = a.getImag() + b.getImag();
    Complex sum (real, imag);
    return sum;
}

Complex multiply (Complex a, Complex b) {
    double mag = a.getMag() * b.getMag();
    double theta = a.getTheta() + b.getTheta();
    Complex product;
    product.setPolar (mag, theta);
    return product;
}

int main(int argc, const char * argv[]) {
    
    Complex c (2.0, 3.0);
    c.printCartesian();
    c.printPolar();
    
    Complex d (17.0, 42.0);
    Complex sum = add (c, d);
    sum.printCartesian();
    
    Complex e (2, 2);
    Complex product = multiply (c, e);
    product.printCartesian();
    
    Complex bad;
    bad.printCartesian();
    
    cout << "I got this far!";
    
    return 0;
}