using System;
using System.Linq;
using System.Collections.Generic;

namespace MandelBrootSet
{
    public struct Complex: IEquatable, IFormattable
    {         
        //Definición de variables de entorno global.
        bool gotMagnitude, gotMagnitudeSquared;
		double magnitude, magnitudeSquared;
		public Complex(double real, double imaginary) : this()
		{
			Real = real;
			Imaginary = imaginary;
		}
		public double Real { private set; get; }
		public double Imaginary { private set; get; }
		//Cálculo del módulo y su cuadrado.
		public double MagnitudeSquared
		{
			get
			{
				if (gotMagnitudeSquared)
				{
					return magnitudeSquared;
				}
				magnitudeSquared = Real * Real + Imaginary * Imaginary;
				gotMagnitudeSquared = true;
				return magnitudeSquared;
			}
		}
		public double Magnitude
		{
			get
			{
				 if (gotMagnitude)
				 {
				 return magnitude;
				 }
				 magnitude = Math.Sqrt(magnitudeSquared);
				 gotMagnitude = true;
				 return magnitude;
			}
		}
		//Sección de Operadores y funciones auxiliares
		public static Complex operator +(Complex left, Complex right)
		 {
			return new Complex(left.Real + right.Real, left.Imaginary + right.Imaginary);
		 }
		 public static Complex operator -(Complex left, Complex right)
		 {
			return new Complex(left.Real - right.Real, left.Imaginary - right.Imaginary);
		 }
		 public static Complex operator *(Complex left, Complex right)
		 {
			return new Complex(left.Real * right.Real - left.Imaginary * right.Imaginary,
			left.Real * right.Imaginary + left.Imaginary * right.Real);
		 }
		 public static bool operator ==(Complex left, Complex right)
		 {
			return left.Real == right.Real && left.Imaginary == right.Imaginary;
		 }
		 public static bool operator !=(Complex left, Complex right)
		 {
			return !(left == right);
		 }
		 public static implicit operator Complex(double value)
		 {
			return new Complex(value, 0);
		 }
		 public static implicit operator Complex(int value)
		 {
			return new Complex(value, 0);
		 }
		 public override int GetHashCode()
		 {
			return Real.GetHashCode() + Imaginary.GetHashCode();
		 }
		 public override bool Equals(Object value)
		 {
			return Real.Equals(((Complex)value).Real) && Imaginary.Equals(((Complex)value).Imaginary);
		 }
		 public bool Equals(Complex value)
		 {
			return Real.Equals(value) && Imaginary.Equals(value);
		 }
		 public override string ToString()
		 {
			return String.Format("{0} {1} {2}i", Real, RealImaginaryConnector(Imaginary), Math.Abs(Imaginary));
		 }
		 public string ToString(string format)
		 {
			return String.Format("{0} {1} {2}i", Real.ToString(format), RealImaginaryConnector(Imaginary), Math.Abs(Imaginary).ToString(format));
		 }
		 public string ToString(IFormatProvider formatProvider)
		 {
			return String.Format("{0} {1} {2}i", Real.ToString(formatProvider), RealImaginaryConnector(Imaginary), Math.Abs(Imaginary).ToString(formatProvider));
		 }
		 public string ToString(string format, IFormatProvider formatProvider)
		 {
			return String.Format("{0} {1} {2}i", Real.ToString(format, formatProvider), RealImaginaryConnector(Imaginary), Math.Abs(Imaginary).ToString(format, formatProvider));
		 }
		 string RealImaginaryConnector(double value)
		 {
			return Math.Sign(value) > 0 ? "+" : "\u2013";
		 }
		 
    }
}