#include <iostream>
#include <math.h>

#include "complexes.h"

using namespace std;

struct complexe saisir_complexe() {
    struct complexe z;

    cout << "Saisir la partie réele" << endl;
    cin >> z.Re;

    cout << "Saisir la partie imaginaire" << endl;
    cin >> z.Im;

    return z;
}

void affiche_complexe(struct complexe z) {
    cout << z.Re << " + (" << z.Im << ")i" << endl;
}

struct complexe conjuge(struct complexe z) {
    return {z.Re, -z.Im};
}

struct complexe oppose(struct complexe z) {
    return {-z.Re, -z.Im};
}

struct complexe inverse(struct complexe z) {
    struct complexe z_inv;
    if (z.Im == 0) {
        z_inv.Im = -z.Im/(z.Re*z.Re + z.Im*z.Im);
    }
    if (z.Re == 0) {
        z_inv.Re = z.Re/(z.Re*z.Re + z.Im*z.Im);
    }

    return z_inv;
}

float module(struct complexe z) {
    float mod = sqrt(pow(z.Re, 2)+pow(z.Im, 2));
    return mod;
}

float argument(struct complexe z) {
    float mod = module(z);
    float arg_abs;
    float arg_sign;

    arg_abs = acos(z.Re/mod);
    arg_sign = asin(z.Im/mod);

    if (arg_sign < 0) {
        return -arg_abs;
    }
    return arg_abs;
}

struct complexe add_complexe(
    struct complexe z,
    struct complexe zp
) {
    return {z.Re + zp.Re, z.Im + zp.Im};
}

struct complexe mult_complexe(
    struct complexe z,
    struct complexe zp
) {
    return {z.Re * zp.Re - z.Im * zp.Im, z.Re * zp.Im + z.Im * zp.Re};
}

struct complexe div_complexe(
    struct complexe z,
    struct complexe zp
) {
    return mult_complexe(z, inverse(zp));
}