?using System;

namespace Mymath
{
    public struct Complex
    {
        /// <summary>
        /// Real part of the complex number
        /// </summary>
        public Double Re;

        /// <summary>
        /// Imaginary part of the complex number
        /// </summary>
        public Double Im;

        /// <summary>
        /// Initializes a new instance of the Complex struct
        /// </summary>
        /// <param name="re">Real part</param>
        /// <param name="im">Imaginary part</param>
        public Complex(Double re, Double im)
        {
            this.Re = re;
            this.Im = im;
        }

        /// <summary>
        /// Initializes a new instance of the Complex struct by copy assignment
        /// </summary>
        /// <param name="rhs">The copy source</param>
        public Complex(Complex rhs)
        {
            this.Re = rhs.Re;
            this.Im = rhs.Im;
        }

        /// <summary>
        /// Represents complex zero
        /// </summary>
        /// <remarks>Represents complex number with both real and imaginary parts equal to zero.</remarks>
        public static Complex Zero
        {
            get { return new Complex(0, 0); }
        }

        /// <summary>
        /// Magnitude value of the complex number
        /// </summary>
        public Double Magnitude
        {
            get { return System.Math.Sqrt(Re * Re + Im * Im); }
        }

        /// <summary>
        /// Squared magnitude value of the complex number
        /// </summary>
        public Double SquaredMagnitude
        {
            get { return (Re * Re + Im * Im); }
        }

        /// <summary>
        /// Phase value of the complex number
        /// </summary>
        public Double Phase
        {
            get { return System.Math.Atan(Im / Re); }
        }

        /// <summary>
        /// Returns string representation of the complex number
        /// </summary>
        /// <returns>String representation of the complex number</returns>
        public override string ToString()
        {
            return String.Format("{0}{1}{2}i", Re, ((Im < 0) ? '-' : '+'), Math.Abs(Im));
        }

        /// <summary>
        /// Addition operator
        /// </summary>
        /// <param name="a">Left complex operand</param>
        /// <param name="b">Right complex operand</param>
        /// <returns>Result complex number</returns>
        public static Complex operator +(Complex a, Complex b)
        {
            return new Complex(a.Re + b.Re, a.Im + b.Im);
        }

        /// <summary>
        /// Subtraction operator
        /// </summary>
        /// <param name="a">Left complex operand</param>
        /// <param name="b">Right complex operand</param>
        /// <returns>Result complex number</returns>
        public static Complex operator -(Complex a, Complex b)
        {
            return new Complex(a.Re - b.Re, a.Im - b.Im);
        }

        /// <summary>
        /// Multiplication operator
        /// </summary>
        /// <param name="a">Left complex operand</param>
        /// <param name="b">Right complex operand</param>
        /// <returns>Result complex number</returns>
        public static Complex operator *(Complex a, Complex b)
        {
            return new Complex(
                a.Re * b.Re - a.Im * b.Im,
                a.Re * b.Im + a.Im * b.Re);
        }

        /// <summary>
        /// Division operator
        /// </summary>
        /// <param name="a">Left complex operand</param>
        /// <param name="b">Right complex operand</param>
        /// <returns>Result complex number</returns>
        public static Complex operator /(Complex a, Complex b)
        {
            double divider = b.Re * b.Re + b.Im * b.Im;

            if (divider == 0)
                throw new DivideByZeroException();

            return new Complex(
                (a.Re * b.Re + a.Im * b.Im) / divider,
                (a.Im * b.Re - a.Re * b.Im) / divider);
        }

        /// <summary>
        /// Conjugate operator
        /// </summary>
        /// <param name="a">Source complex operand</param>
        /// <returns>Result complex conjugate</returns>
        public static Complex operator ~(Complex a)
        {
            return new Complex(a.Re, -a.Im);
        }

        /// <summary>
        /// Equation operator
        /// </summary>
        /// <param name="a">Left complex operand</param>
        /// <param name="b">Right complex operand</param>
        /// <returns>The two complex operands are equal or not</returns>
        public static Boolean operator ==(Complex a, Complex b)
        {
            return a.Re == b.Re && a.Im == b.Im;
        }

        public static Boolean operator !=(Complex a, Complex b)
        {
            return a.Re != b.Re || a.Im != b.Im;
        }

        public override bool Equals(object obj)
        {
            return this == (Complex)obj;
        }

        public override int GetHashCode()
        {
            return base.GetHashCode();
        }
    }
}