New Version 6.0!

Try it for free with our fully functional 60-day trial version.

Download now!

QuickStart Samples

Complex Numbers QuickStart Sample (C#)

Illustrates how to work with complex numbers using the DoubleComplex structure in C#.

Visual Basic code F# code IronPython code Back to QuickStart Samples

using System;

namespace Extreme.Numerics.QuickStart.CSharp
{
    // The Complex<double> class resides in the Extreme.Mathematics namespace.
    using Extreme.Mathematics;

    /// <summary>
    /// Illustrates the use of the Complex<double> class in the
    /// Extreme Optimization Mathematics Library for .NET.
    /// </summary>
    class ComplexNumbers
    {

        /// <summary>
        /// The main entry point for the application.
        /// </summary>
        [STAThread]
        static void Main(string[] args)
        {
            //
            // Complex<double> constants:
            //
            Console.WriteLine("Complex<double>.Zero = {0}", Complex<double>.Zero);
            Console.WriteLine("Complex<double>.One = {0}", Complex<double>.One);
            // The imaginary unit is given by Complex<double>.I:
            Console.WriteLine("Complex<double>.I = {0}", Complex<double>.I);
            Console.WriteLine();

            //
            // Construct some complex numbers
            //
            // Real and imaginary parts:
            //   a = 2 + 4i
            Complex<double> a = new Complex<double>(2, 4);
            Console.WriteLine("a = {0}", a);
            //   b = 1 - 3i
            Complex<double> b = new Complex<double>(1, -3);
            Console.WriteLine("b = {0}", b.ToString());
            // From a real number:
            //   c = -3 + 0i
            Complex<double> c = new Complex<double>(-3);
            Console.WriteLine("c = {0}", c.ToString());
            // Polar form:
            //   d = 2 (cos(Pi/3) + i sin(Pi/3))
            Complex<double> d = Complex<double>.FromPolar(2, Constants.Pi/3);
            // To print this number, use the overloaded ToString
            // method and specify the format string for the real 
            // and imaginary parts:
            Console.WriteLine("d = {0}", d);
            Console.WriteLine();

            //
            // Parts of complex numbers
            //
            Console.WriteLine("Parts of a = {0}:", a);
            Console.WriteLine("Real part of a = {0}", a.Re);
            Console.WriteLine("Imaginary part of a = {0}", a.Im);
            Console.WriteLine("Modulus of a = {0}", a.Magnitude);
            Console.WriteLine("Argument of a = {0}", a.Phase);
            Console.WriteLine();

            //
            // Basic arithmetic:
            //
            Console.WriteLine("Basic arithmetic:");
            Complex<double> e = -a;
            Console.WriteLine("-a = {0}", e);
            e = a + b;
            Console.WriteLine("a + b = {0}", e);
            e = a - b;
            Console.WriteLine("a - b = {0}", e);
            e = a * b;
            Console.WriteLine("a * b = {0}", e);
            e = a / b;
            Console.WriteLine("a / b = {0}", e);
            // The conjugate of a complex number corresponds to
            // the "Conjugate" method:
            e = a.Conjugate();
            Console.WriteLine("Conjugate(a) = ~a = {0}", e);
            Console.WriteLine();

            //
            // Functions of complex numbers
            //
            // Most of these have corresponding static methods 
            // in the System.Math class, but are extended to complex 
            // arguments.
            Console.WriteLine("Functions of complex numbers:");

            // Exponentials and logarithms
            Console.WriteLine("Exponentials and logarithms:");
            e = Complex<double>.Exp(a);
            Console.WriteLine("Exp(a) = {0}", e);
            e = Complex<double>.Log(a);
            Console.WriteLine("Log(a) = {0}", e);
            e = Complex<double>.Log10(a);
            Console.WriteLine("Log10(a) = {0}", e);
            // You can get a point on the unit circle by calling
            // the ExpI method:
            e = Complex<double>.ExpI(2*Constants.Pi/3);
            Console.WriteLine("ExpI(2*Pi/3) = {0}", e);
            // The RootOfUnity method also returns points on the
            // unit circle. The above is equivalent to the second
            // root of z^6 = 1:
            e = Complex<double>.RootOfUnity(6, 2);
            Console.WriteLine("RootOfUnity(6, 2) = {0}", e);


            // The Pow method is overloaded for integer, double,
            // and complex argument:
            e = Complex<double>.Pow(a, 3);
            Console.WriteLine("Pow(a,3) = {0}", e);
            e = Complex<double>.Pow(a, 1.5);
            Console.WriteLine("Pow(a,1.5) = {0}", e);
            e = Complex<double>.Pow(a, b);
            Console.WriteLine("Pow(a,b) = {0}", e);

            // Square root
            e = Complex<double>.Sqrt(a);
            Console.WriteLine("Sqrt(a) = {0}", e);
            // The Sqrt method is overloaded. Here's the square 
            // root of a negative double:
            e = Complex<double>.Sqrt(-4);
            Console.WriteLine("Sqrt(-4) = {0}", e);
            Console.WriteLine();

            //
            // Trigonometric functions:
            //
            Console.WriteLine("Trigonometric function:");
            e = Complex<double>.Sin(a);
            Console.WriteLine("Sin(a) = {0}", e);
            e = Complex<double>.Cos(a);
            Console.WriteLine("Cos(a) = {0}", e);
            e = Complex<double>.Tan(a);
            Console.WriteLine("Tan(a) = {0}", e);

            // Inverse Trigonometric functions:
            e = Complex<double>.Asin(a);
            Console.WriteLine("Asin(a) = {0}", e);
            e = Complex<double>.Acos(a);
            Console.WriteLine("Acos(a) = {0}", e);
            e = Complex<double>.Atan(a);
            Console.WriteLine("Atan(a) = {0}", e);

            // Asin and Acos have overloads with real argument
            // not restricted to [-1,1]:
            e = Complex<double>.Asin(2);
            Console.WriteLine("Asin(2) = {0}", e);
            e = Complex<double>.Acos(2);
            Console.WriteLine("Acos(2) = {0}", e);
            Console.WriteLine();
            
            //
            // Hyperbolic and inverse hyperbolic functions:
            //
            Console.WriteLine("Hyperbolic function:");
            e = Complex<double>.Sinh(a);
            Console.WriteLine("Sinh(a) = {0}", e);
            e = Complex<double>.Cosh(a);
            Console.WriteLine("Cosh(a) = {0}", e);
            e = Complex<double>.Tanh(a);
            Console.WriteLine("Tanh(a) = {0}", e);
            e = Complex<double>.Asinh(a);
            Console.WriteLine("Asinh(a) = {0}", e);
            e = Complex<double>.Acosh(a);
            Console.WriteLine("Acosh(a) = {0}", e);
            e = Complex<double>.Atanh(a);
            Console.WriteLine("Atanh(a) = {0}", e);
            Console.WriteLine();

            Console.Write("Press Enter key to exit...");
            Console.ReadLine();
        }
    }
}