#ifndef _COMPLEX_H
#define _COMPLEX_H
#include <iostream>
#include <cmath>

class Complex {
    private:
        double re, im;

    public:
        Complex( double, double );

        // Accessors
        double real() const;
        double imag() const;
        double abs() const;
        Complex exp() const;

        // Mutators
        void normalize();

    friend std::ostream & operator << ( std::ostream &, const Complex & );
};

// Constructor
Complex::Complex( double r, double i ):re(r), im(i) {
    // empty constructor
}
// return the real component
double Complex::real() const {
    return re;
}

// return the imaginary component
double Complex::imag() const {
    return im;
}

// return the absolute value
double Complex::abs() const {
    return sqrt( re*re + im*im );
}

// return the exponential of the complex value
Complex Complex::exp() const {
    double exp_re = std::exp( re );

    return Complex( exp_re*std::cos(im), exp_re*std::sin(im) );
}

// normalize the complex number (giving it unit norm, |z| = 1)
void Complex::normalize() {
    if ( re == 0 && im == 0 ) {
        return;
    }

    double absval = abs();
    re /= absval;
    im /= absval;
}

std::ostream & operator << ( std::ostream & out, const Complex & z ) {
    if ( z.im > 0 ) {
        if ( z.re == 0 ) {
            out << z.im << 'j';                          // 4j
        } else {
            out << z.re << " + " << z.im << 'j';         // 3 + 4j
        }
    } else if ( z.im == 0 ) {
        out << z.re;                                     // 3
    } else {  // z.im < 0
        if ( z.re == 0 ) {
            out << z.im << 'j';                          // -4j
        } else {
            out << z.re << " - " << (-z.im) << 'j';      // 3 - 4j
        }
    }

    return out;
}

#endif