C# Complex Numbers

[jballen87]

I'm trying to create a program in C# that allows for arithmetic of Complex Numbers. Just adding, subtracting, multiplying and dividing. Anyone got any suggestions?

[jonsca]

Create your own class with + - * / overloaded.

This is an example for matrices but it's similar (complex will be less complicated).

Give it a go and post back when you get stuck (or if you have code already post it and someone can look it over).

[ddanbe]

This is how I did it some months ago :

using System;

namespace MarMath
{
    /// <summary>
    /// 
    /// 
    /// struct for complex numbers
    /// 
    /// See also [url]http://en.wikipedia.org/wiki/Complex_number[/url]
    /// A collection of as much functions and issues I could find about it on the web.
    /// Special thanks to Scott Knake for his assistance on IFormattable and IConvertible.
    /// © Euler, DeMoivre and others...
    /// 
    /// Version 1.00                8 augustus 2009
    /// 
    /// Danny Marivoet
    /// 
    /// </summary>
    struct Complex : IFormattable, IConvertible
    {
        #region Fields.

        /// <summary>
        /// The real and imaginary parts of this struct
        /// If the imaginary part is zero then a complex number is a real number.
        /// The imaginary part is always multiplied with a constant mostly called i.
        /// i^2 = -1
        /// </summary>
        private double _real, _imag;

        // A static random field which uses a timeseed
        private static Random rnd = new Random(); 

        #endregion

        #region Complex contructors.

        /// <summary>
        /// Initialize a complex number with a real and imaginary part
        /// </summary>
        /// <param name="real"></param>
        /// <param name="imag"></param>
        public Complex(double real, double imag)
        {
            this._real = real; this._imag = imag;
        }

        /// <summary>
        /// Create a new complex number out of an existing one
        /// </summary>
        /// <param name="z"></param>
        public Complex(Complex z)
        {
            this._real = z.realpart; this._imag = z.imaginarypart;
        } 
        #endregion
 
        #region Properties.

        /// <summary>
        /// Get the real part of a complex number.
        /// </summary>
        public double realpart
        {
            get { return _real; }
            set { _real = value; }
        }

        /// <summary>
        /// Get the imaginary part of a complex number.
        /// </summary>
        public double imaginarypart
        {
            get { return _imag; }
            set { _imag = value; }
        }

        /// <summary>
        /// I^2 is equal to -1.
        /// </summary>
        public static Complex I
        {
            get { return new Complex(0.0, 1.0); }
        }

        /// <summary>
        /// Return a zero comlex number
        /// </summary>
        public static Complex Zero
        {
            get { return new Complex(0.0, 0.0); }
        }

        /// <summary>
        /// Get the complex conjugate of a complex number.
        /// It is obtained by changing the sign of the imaginary part.
        /// </summary>
        public Complex Conjugate
        {
            get { return new Complex(_real, -_imag); }
        }

        /// <summary>
        /// Also called Norm or absolute value.
        /// </summary>
        public double Modulus
        {
            get { return System.Math.Sqrt(_real * _real + _imag * _imag); }
        }

        /// <summary>
        /// Returns the square of the Modulus
        /// </summary>
        public double AbsoluteSquare
        {
            get { return _real * _real + _imag * _imag; }
        }

        /// <summary>
        /// Also called angle.
        /// </summary>
        public double Argument
        {
            get 
            {
                if (_imag == 0 && _real < 0)
                    return Math.PI;
                if (_imag == 0 && _real >= 0)
                    return 0;
                return System.Math.Atan2(_imag, _real); 
            }
        }

        /// <summary>
        /// Returns one divided by the current value.
        /// </summary>
        public Complex Reciprocal
        {
            get
            {
                if (_real == 0d && _imag == 0d)
                    throw new DivideByZeroException();

                double div = _real * _real + _imag * _imag;
                return new Complex(_real / div, -_imag / div);
            }
        }

        #endregion

This is just the start and not the complete code. I leave it to you to implement the operator overloading. You will also have to override the ToString method, because of the special format of complex numbers when written.