The Modulus of a Complex Number:

This function computes the modulus of z = a + ib and returns the double $\sqrt{a^2 + b^2}$.

//====================================================//
//                                                    //
//                modulus                             //
//                                                    //
//====================================================//
double modulus(const MYCOMPLEX &w)
{
double modulus = w.real*w.real + w.imaginary*w.imaginary;
return (sqrt(modulus));
}

\subsection{The Argument of a Complex Number:}

The complex number $z = a + ib$ cna be written in the
form $z = r e ^{i\theta}$, where $r$ is the modulus of $z$
and $\theta$ is the argument of $z$.  We compute a particular
branch of this argument by restricting our attentions to
arguments given by the default range of the built in
function $atan2()$.

\small \begin{verbatim}
//====================================================//
//                                                    //
//                arg                                 //
//                                                    //
//====================================================//

double arg(const MYCOMPLEX &w)
{ 
  if(w.imaginary == 0.0){
    if(w.real>0.0) return(0.0);
    else if (w.real < 0.0) return(PI);
    else{
      cout << "Arg for w = 0+0i is undefined";
      cout << " returning arg = 10^6" << endl;
      return(1.0e6);
      }
    }
  else if(w.real == 0.0){
    if(w.imaginary>0.0) return(.5*PI);
    else if (w.imaginary < 0.0) return(1.5*PI);
    else{
      cout << "Arg for w = 0+0i is undefined";
      cout << " returning arg = 10^6" << endl;
      return(1.0e6);
      }
    }
   else{
     return(atan2(w.imaginary,w.real));
     }
}