# Complex Numbers in Visual Basic QuickStart Sample

Illustrates how to work with complex numbers using the DoubleComplex structure in Visual Basic.

View this sample in: C# F# IronPython

``````Option Infer On

' The Complex(Of T) class resides in the Extreme.Mathematics namespace.
Imports Extreme.Mathematics

' Illustrates the use of the Complex(Of Double) class in the
' Extreme Numerics.NET.
' </summary>
Module ComplexNumbers

Sub Main()
' The license is verified at runtime. We're using
' https://numerics.net/trial-key

'
' Complex(Of Double) constants:
'
Console.WriteLine("Complex(Of Double).Zero = {0}", Complex(Of Double).Zero)
Console.WriteLine("Complex(Of Double).One = {0}", Complex(Of Double).One)
' The imaginary unit is given by Complex(Of Double).I:
Console.WriteLine("Complex(Of Double).I = {0}", Complex(Of Double).I)
Console.WriteLine()

'
' Construct some complex numbers
'
' Real and imaginary parts:
'   a = 2 + 4i
Dim a As New Complex(Of Double)(2, 4)
Console.WriteLine("a = {0}", a)
'   b = 1 - 3i
Dim b As New Complex(Of Double)(1, -3)
Console.WriteLine("b = {0}", b.ToString())
' From a real number:
'   c = -3 + 0i
Dim c As New Complex(Of Double)(-3)
Console.WriteLine("c = {0}", c.ToString())
' Polar form:
'   d = 2 (cos(Pi/3) + i sin(Pi/3))
Dim d = Complex(Of 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.ToString("F4"))
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:")
Dim e As Complex(Of 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)
e = a.Conjugate
Console.WriteLine("Conjugate(a) = {0}", e)
Console.WriteLine()

'
' Functions of complex numbers
'
' Most of these have corresponding Shared 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(Of Double).Exp(a)
Console.WriteLine("Exp(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Log(a)
Console.WriteLine("Log(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Log10(a)
Console.WriteLine("Log10(a) = {0}", e.ToString("F4"))
' You can get a point on the unit circle by calling
' the ExpI method:
e = Complex(Of Double).ExpI(2 * Constants.Pi / 3)
Console.WriteLine("ExpI(2*Pi/3) = {0}", e.ToString("F4"))
' The RootOfUnity method also returns points on the
' unit circle. The above is equivalent to the second
' root of z^6 = 1:
e = Complex(Of Double).RootOfUnity(6, 2)
Console.WriteLine("RootOfUnity(6, 2) = {0}", e.ToString("F4"))

' The Pow method is overloaded for integer, double,
' and complex argument:
e = Complex(Of Double).Pow(a, 3)
Console.WriteLine("Pow(a,3) = {0}", e.ToString("F4"))
e = Complex(Of Double).Pow(a, 1.5)
Console.WriteLine("Pow(a,1.5) = {0}", e.ToString("F4"))
e = Complex(Of Double).Pow(a, b)
Console.WriteLine("Pow(a,b) = {0}", e.ToString("F4"))

' Square root
e = Complex(Of Double).Sqrt(a)
Console.WriteLine("Sqrt(a) = {0}", e.ToString("F4"))
' The Sqrt method is overloaded. Here's the square
' root of a negative double:
e = Complex(Of Double).Sqrt(-4)
Console.WriteLine("Sqrt(-4) = {0}", e.ToString("F4"))
Console.WriteLine()

'
' Trigonometric functions:
'
Console.WriteLine("Trigonometric function:")
e = Complex(Of Double).Sin(a)
Console.WriteLine("Sin(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Cos(a)
Console.WriteLine("Cos(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Tan(a)
Console.WriteLine("Tan(a) = {0}", e.ToString("F4"))

' GetInverse Trigonometric functions:
e = Complex(Of Double).Asin(a)
Console.WriteLine("Asin(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Acos(a)
Console.WriteLine("Acos(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Atan(a)
Console.WriteLine("Atan(a) = {0}", e.ToString("F4"))

' Asin and Acos have overloads with real argument
' not restricted to [-1,1]:
e = Complex(Of Double).Asin(2)
Console.WriteLine("Asin(2) = {0}", e.ToString("F4"))
e = Complex(Of Double).Acos(2)
Console.WriteLine("Acos(2) = {0}", e.ToString("F4"))
Console.WriteLine()

'
' Hyperbolic and inverse hyperbolic functions:
'
Console.WriteLine("Hyperbolic function:")
e = Complex(Of Double).Sinh(a)
Console.WriteLine("Sinh(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Cosh(a)
Console.WriteLine("Cosh(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Tanh(a)
Console.WriteLine("Tanh(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Asinh(a)
Console.WriteLine("Asinh(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Acosh(a)
Console.WriteLine("Acosh(a) = {0}", e.ToString("F4"))
e = Complex(Of Double).Atanh(a)
Console.WriteLine("Atanh(a) = {0}", e.ToString("F4"))
Console.WriteLine()

Console.Write("Press Enter key to exit...")