Operator Overloading I

/*This code was written by A. El-Gadi of Tripoli University for educational purposes. It uses operator overloading to implement vector addition, subtraction, negation, and scaling. For any questions use the comment section below.*/

#include<iostream>
#include<stdlib.h>
#include<cmath>

using namespace std;

const double pi=3.14159;

class Vec{
private:
    double magnitude;
    double angle;
public:

//Accessor and mutator member functions go here.
    Vec(){magnitude=0; angle=0;}
    Vec(double mag,double angle):magnitude(mag),angle(angle){};
   
    Vec operator+(Vec vright){double xleft, yleft, xright, yright, newmag, newang;
                    xleft=magnitude*cos(angle);
                    yleft=magnitude*sin(angle);
                    xright=vright.magnitude*cos(vright.angle);
                    yright=vright.magnitude*sin(vright.angle);
                    newmag=sqrt(pow(xleft+xright,2)+pow(yleft+yright,2));
                    newang=asin((yleft+yright)/newmag);
                    return Vec(newmag,newang);}
    Vec operator-(Vec vright){return *this+Vec(vright.magnitude,vright.angle+pi);}
    Vec operator-(){return Vec(magnitude,angle+pi);}
    friend Vec operator*(double,Vec);
    friend Vec operator*(Vec,double);
    void show(){cout<<magnitude<<' '<<angle<<'\n';}
    };

Vec operator*(double scalar,Vec vr){return Vec(scalar*vr.magnitude,vr.angle);}
Vec operator*(Vec vl,double scalar){return Vec(scalar*vl.magnitude,vl.angle);}

int main(){

Vec v1(4,0), v2(3,pi/2);
Vec v3;

v1.show(); v2.show();
(v1+v2).show();
(v2+v1).show();

(v1+(-v2)).show();
(v1-v2).show();

v3=-v1+v2-3*v1+1.7*v2+v2*2.3;

v3.show();

(-v3).show();

(3.4*v3*2.3).show();

return 0;
}