// complessi.c
# include "alfa.h"

nc Ncadd (nc z1, nc z2)
{nc w;
w.x=z1.x+z2.x; w.y=z1.y+z2.y;
return w;}

nc Nccon (nc z)
{z.y=-z.y; return z;}

nc Nccos (nc z)
{nc w={cosh(z.y)*cos(z.x),
  -sinh(z.y)*sin(z.x)};
return w;}

nc Ncdiv (nc z1, nc z2)
{double q,t; nc w;
if (fabs(z2.x)>=fabs(z2.y))
{q=z2.y/z2.x; t=z2.x+z2.y*q;
w.x=(z1.x+z1.y*q)/t;
w.y=(z1.y-z1.x*q)/t;
return w;}
q=z2.x/z2.y; t=z2.x*q+z2.y;
w.x=(z1.x*q+z1.y)/t;
w.y=(z1.y*q-z1.x)/t;
return w;}

nc Ncexp (nc z)
{double ex=exp(z.x);
nc w={ex*cos(z.y),ex*sin(z.y)};
return w;}

nc Ncmolt (nc z1, nc z2)
{nc w;
w.x=z1.x*z2.x-z1.y*z2.y;
w.y=z1.x*z2.y+z2.x*z1.y;
return w;}

nc Ncsin (nc z)
{nc w={cosh(z.y)*sin(z.x),
  sinh(z.y)*cos(z.x)};
return w;}

nc Ncsott (nc z1, nc z2)
{nc w;
w.x=z1.x-z2.x; w.y=z1.y-z2.y;
return w;}

double Ncva (nc z)
{double vax,vay,t;
if (z.x==0) return fabs(z.y);
if (z.y==0) return fabs(z.x);
vax=fabs(z.x); vay=fabs(z.y);
if (vax>=vay)
{t=z.y/z.x; return vax*sqrt(1+t*t);}
t=z.x/z.y; return vay*sqrt(1+t*t);}