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

class Complex {
private:
    double real, imag;
    double mag, theta;
    bool cartesian, polar;
    void calculateCartesian ();
    void calculatePolar ();

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

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

    double getReal ();
    double getImag ();
    void printCartesian ();
    double getMag ();
    double getTheta ();
    void printPolar ();
    void setPolar (double m, double t);
};

void Complex::calculateCartesian ()
{
    if (polar == false) {
        cout <<
        "calculateCartesian failed because the polar representation is invalid"
        << endl;
        exit (1);
    }
    real = mag * cos (theta);
    imag = mag * sin (theta);
    cartesian = true;
}

void Complex::calculatePolar ()
{
    assert (cartesian); // precondition for calculatePolar
    mag = sqrt ( real*real + imag*imag);
    theta = atan2 (imag, real);
    polar = true;
    assert (polar && cartesian); // postcondition
}

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

double Complex::getImag ()
{
    if (cartesian == false) calculateCartesian ();
    return imag;
}

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

double Complex::getMag ()
{
    if (polar == false) calculatePolar ();
    return mag;
}

double Complex::getTheta ()
{
    if (polar == false) calculatePolar ();
    return theta;
}

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

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

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

Complex mult (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 () {
    Complex c1 (2.0, 3.0);

    c1.printCartesian();
    c1.printPolar();

    c1.setPolar(1, 3.14159/2);
    c1.printCartesian();
    c1.printPolar();

    Complex c2 (3.0, 4.0);

    Complex sum = add (c1, c2);
    sum.printCartesian();
    Complex product = mult (c1, c2);
    product.printCartesian();

    Complex cBad;
    cBad.printPolar();


    return 0;
}