/*
 * complex.c implements some complex arithmetic
 *
 */
#include <assert.h>
#include <math.h>
#include "complex.h"

struct cpoint cplus(struct cpoint z1, struct cpoint z2)
{
  struct cpoint sum = z1;
  sum.x += z2.x;
  sum.y += z2.y;
  return sum;
}

struct cpoint ctimes(struct cpoint z1, struct cpoint z2)
{
    struct cpoint product = z1;
    
    product.x *= z2.x;
    product.x -= z1.y * z2.y;
    product.y = z1.x * z2.y + z1.y * z2.x;
   
    return product;
}

double mag(struct cpoint z)
{
    return sqrt(z.x * z.x + z.y * z.y);
}

struct cpoint conj(struct cpoint z)
{
    z.y *= -1;
    return z;
}

struct cpoint cdiv(struct cpoint z1, struct cpoint z2)
{
    struct cpoint quotient = z1;
    double magsquared = z2.x * z2.x + z2.y * z2.y;

    assert(magsquared != 0); /* or crash informatively */
    quotient = ctimes(z1, conj(z2));
    quotient.x /= magsquared;
    quotient.y /= magsquared;

    return quotient;
}