/*

	Classe COMPLEXE
	Gestion des nombres Complexes
	Version 1.1 - Last Modif : 22/02/2007 15:52
	Développé par SeBeuH < sebeuh [arobase] ajsinfo [point].net >
	(c) 2006-2007 - http://sebeuh.ajsinfo.net

*/
using System;
using System.Collections.Generic;
using System.Text;
using System.Drawing;

namespace Complexes
{
    public class Complexe
    {
        #region Champs privés

        private double _reel;
        private double _imaginaire;

        #endregion

        #region Constructeurs

        public Complexe() : this(0, 0) { }
        public Complexe(Point point) : this(point.X, point.Y) { }
        public Complexe(double reel, double imaginaire) {
            this._reel = reel;
            this._imaginaire = imaginaire;
        }

        #endregion

        #region ToString

        // Renvoi du complexe sous la forme a+ib
        public override string ToString() {
            StringBuilder cmpStr = new StringBuilder();
            if(this._reel != 0)
                cmpStr.Append((float)this._reel);
            if (this._imaginaire > 0 && this._imaginaire != 1)
                cmpStr.Append(String.Format("+{0}i", ((float)this._imaginaire).ToString()));
            else if (this._imaginaire == 1)
                cmpStr.Append("+i");
            else if (this._imaginaire < 0 && this._imaginaire != -1)
                cmpStr.Append(String.Format("{0}i", ((float)this._imaginaire).ToString()));
            else if (this._imaginaire == -1)
                cmpStr.Append("-i");
            return cmpStr.ToString();
        }


        #endregion

        #region Surcharge des operateurs

        //  Addition
        public static Complexe operator +(Complexe c1, Complexe c2) {
            return (new Complexe((c1.Reel + c2.Reel), (c1.Imaginaire + c2.Imaginaire)));
        }
        //  Soustraction
        public static Complexe operator -(Complexe c1, Complexe c2) {
            return (new Complexe((c1.Reel - c2.Reel), (c1.Imaginaire - c2.Imaginaire)));
        }
        //  Multiplication
        public static Complexe operator *(Complexe c1, Complexe c2) {
            return (new Complexe(((c1.Reel * c2.Reel) - (c1.Imaginaire * c2.Imaginaire)), ((c1.Reel * c2.Imaginaire) + (c2.Reel * c1.Imaginaire))));
        }
        //  Division
        public static Complexe operator /(Complexe c1, Complexe c2) {
            return (new Complexe(((c1._reel * c2._reel - c1._imaginaire * (-c2._imaginaire)) / (Math.Pow(c2._reel, 2) + Math.Pow(c2._imaginaire, 2))), ( ((c1._reel * (-c2._imaginaire) + c2._reel * c1._imaginaire) / (Math.Pow(c2._reel, 2) + Math.Pow(c2._imaginaire, 2))))));
        }

        #endregion

        #region Methodes

        //  Rotation
        public Complexe Rotation(double angle, Complexe centre) {
            return (((this - centre) * (new Complexe(Math.Cos(angle), Math.Sin(angle)))) + centre);
        }

        #endregion

        #region Accesseurs en Get (read only)

        //  Conjugué du complexe
        public Complexe Conjugue {
            get { return new Complexe(this._reel, (0 - this._imaginaire)); }
        }
        //  Module du complexe
        public double Module {
            get { return Math.Sqrt((Math.Pow(this._reel, 2) + Math.Pow(this._imaginaire, 2))); }
        }
        //  Argument du complexe
        public double Argument {
            get { return (Math.Atan((this._imaginaire / this._reel))); }
        }
        //  Carré du complexe
        public Complexe Carre {
            get { return new Complexe((Math.Pow(this._reel,2)-Math.Pow(this._imaginaire,2)),(2*this._reel*this._imaginaire)); }
        }

        #endregion

        #region Accesseurs en Get&Set
        //  Partie Reel
        public double Reel {
            get { return this._reel; }
            set { this._reel = value; }
        }
        //  Partie Imaginaire
        public double Imaginaire {
            get { return this._imaginaire; }
            set { this._imaginaire = value; }
        }
        // Point
        public Point Point {
            get {
                return new Point((int)this._reel, (int)this._imaginaire);
            }
            set {
                this._reel = value.X;
                this._imaginaire = value.Y;
            }
        }

        #endregion
    }
}