// Complex Newton method
#include <stdio.h>
#include <math.h>
#include <complex.h>
#define NUMAX 10  // maximum number of iteration
#define EPS 1.0e-12 // If |f(z_i)|< EPS then stop.
double complex f(double complex z);  /* f(z) */
double complex df(double complex z);  /* f'(z) */

int main(void)
{
  int nu;
  double absfz; 
  double complex z,u,fz,dfz;

  z = -1.0 + 1.0 * I;
  
  nu = 0;
  absfz = cabs(f(z));
  printf("%2s %20s %19s %10s\n","nu","Re(z_nu)  ","Im(z_nu)  ","|f(z_nu)|");
  printf("%2d %20.15f %19.15f %10.3e\n",nu,creal(z),cimag(z),absfz); 
 
  while(absfz>EPS && nu<NUMAX)
    {
      fz = f(z);
      dfz = df(z);
      u = fz/dfz;
      z = z - u;
      nu++;
      absfz=cabs(f(z));
      printf("%2d %20.15f %19.15f %10.3e\n",nu,creal(z),cimag(z),absfz); 
    }
  
  return 0;
}

double complex f(double complex z)
{
  double complex w;

  w = -5.0 + z * (-2.0 + z * z);

  return w;
}


double complex df(double complex z)
{
  double complex w;

  w = -2.0 + 3.0 * z * z;

  return w;
}