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QuickStart Samples

# Complex Numbers QuickStart Sample (C#)

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

```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>
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...");