/* Cmplx.h header file for complex number class */

class Cmplx {
public:
      double real;
      double imag; // private members by default

public:

      Cmplx(double InitR, double InitI); // a constructor for the class
      Cmplx(){real=0.0;imag=0.0;} //default constructor, overloaded
      Cmplx(double r){real=r;imag=0.0;}// real number constructor
      Cmplx operator+(Cmplx);     // four overloaded operators
      Cmplx operator*(Cmplx);     // for +,-,*,/
      Cmplx operator-(Cmplx);
      Cmplx operator/(Cmplx);
      double Re(){return real;} // an inlined method
      double Im(){return imag;}
      double Modulus();
      double Phase();
};

double Cmplx::Modulus()
              {
              return(sqrt(real*real+imag*imag));
              }
double Cmplx::Phase()
              {
              return(atan2(imag,real));
              }
Cmplx::Cmplx(double InitR, double InitI)
             {
             real=InitR;
             imag=InitI;
             }
Cmplx Cmplx::operator+(Cmplx z_add)
             {
             Cmplx temp(0,0);
             temp.real=real+z_add.real;
             temp.imag=imag+z_add.imag;
             return temp;
             }
Cmplx Cmplx::operator-(Cmplx z_add)
             {
             Cmplx temp(0,0);
             temp.real=real-z_add.real;
             temp.imag=imag-z_add.imag;
             return temp;
             }
Cmplx Cmplx::operator*(Cmplx z_add)
             {
             Cmplx temp(0,0);
             temp.real=real*z_add.real-imag*z_add.imag;
             temp.imag=imag*z_add.real+real*z_add.imag;
             return temp;
             }
Cmplx Cmplx::operator/(Cmplx z_add)
             {
             Cmplx temp(0,0);
             double factor=z_add.Modulus();
             double denom=factor*factor;
             temp.real=(real*z_add.real+imag*z_add.imag)/denom;
             temp.imag=(imag*z_add.real-real*z_add.imag)/denom;
             return temp;
             }


Cmplx Csin(Cmplx a)
{
Cmplx z(0,0);
z.real=sin(a.real)*cosh(a.imag);
z.imag=cos(a.real)*sinh(a.imag);
return z;
}
 
Cmplx Ccos(Cmplx a)
{
Cmplx z(0,0);
z.real=cos(a.real)*cosh(a.imag);
z.imag=-sin(a.real)*sinh(a.imag);
return z;
}

Cmplx Cexp(Cmplx a)
{
Cmplx z(0,0);
double factor =exp(a.real);
z.real=factor*cos(a.imag);
z.imag=factor*sin(a.imag);
return z;
}

Cmplx Clog(Cmplx a)
{
Cmplx z(0,0);
z.real=0.5*log(a.Modulus());
z.imag=atan2(a.imag, a.real);
return z;
}

// Here we overload the insertion operator to output Cmplx
ostream& operator<<(ostream& str, Cmplx& z)
{
  str<<z.real<<"+"<<z.imag<<" i";
return str;
// notice that we return an ostream& object
}