Handling Complex Numbers in C

#include <stdio.h>
#include <math.h>
#include "COMPLEX.h"
#define PI 3.141592625
main(int argc, char *argv[])
  { int i, j, N = atoi(argv[1]);
    Complex t, x;
    printf("%dth complex roots of unity\n", N);
    for (i = 0; i < N; i++)
      { float r = 2.0*PI*i/N;
        t = COMPLEXinit(cos(r), sin(r));
        printf("%2d %6.3f %6.3f ", i, Re(t), Im(t));
        for (x = t, j = 0; j < N-1; j++)
          x = COMPLEXmult(t, x);
        printf("%6.3f %6.3f\n", Re(x), Im(x));
      }
 }
-----
typedef struct { float Re; float Im; } Complex;
Complex COMPLEXinit(float, float);
  float Re(Complex);
  float Im(Complex);
Complex COMPLEXmult(Complex, Complex);
-----
#include "COMPLEX.h"
Complex COMPLEXinit(float Re, float Im)
  { Complex t; t.Re = Re; t.Im = Im; return t; }
float Re(Complex z)
  { return z.Re; }
float Im(Complex z)
  { return z.Im; }
Complex COMPLEXmult(Complex a, Complex b)
  { Complex t; 
    t.Re = a.Re*b.Re - a.Im*b.Im; 
    t.Im = a.Re*b.Im + a.Im*b.Re; 
    return t; 
  }
-----
typedef struct complex *Complex;
Complex COMPLEXinit(float, float);
  float Re(Complex);
  float Im(Complex);
Complex COMPLEXmult(Complex, Complex);
-----
#include <stdlib.h>
#include "COMPLEX.h"
struct complex { float Re; float Im; };
Complex COMPLEXinit(float Re, float Im)
  { Complex t = malloc(sizeof *t); 
    t->Re = Re; t->Im = Im; 
    return t; 
  }
float Re(Complex z)
  { return z->Re; }
float Im(Complex z)
  { return z->Im; }
Complex COMPLEXmult(Complex a, Complex b)
  { 
    return COMPLEXinit(Re(a)*Re(b) - Im(a)*Im(b),  
                       Re(a)*Im(b) + Im(a)*Re(b));
  }