VB.Net Tutorial/Data Type/Complex Number

Complex

public class Test
   public Shared Sub Main
        Dim X, Y As Complex
        X = New Complex(1, 4)
        Y = New Complex(2, 3)
        Console.WriteLine((X + Y).ToString)
        Console.WriteLine((X - Y).ToString)
        Console.WriteLine((X * Y).ToString)
        Console.WriteLine((X = Y).ToString)
        Console.WriteLine((X <> Y).ToString)
        Console.WriteLine((-X).ToString)
        Dim abs_x As Double = CDbl(X)
        Console.WriteLine(abs_x.ToString)
   End Sub
End class

Public Class Complex
    Public Re As Double
    Public Im As Double
    Public Sub New()
    End Sub
    Public Sub New(ByVal real_part As Double, ByVal imaginary_part As Double)
        Re = real_part
        Im = imaginary_part
    End Sub
    Public Overrides Function ToString() As String
        Return Re.ToString & " + " & Im.ToString & "i"
    End Function
    Public Shared Operator *(ByVal c1 As Complex, ByVal c2 As Complex) As Complex
        Return New Complex( _
            c1.Re * c2.Re - c1.Im * c2.Im, _
            c1.Re * c2.Im + c1.Im * c2.Re)
    End Operator
    Public Shared Operator +(ByVal c1 As Complex, ByVal c2 As Complex) As Complex
        Return New Complex( c1.Re + c2.Re,c1.Im + c2.Im)
    End Operator
    Public Shared Operator -(ByVal c1 As Complex, ByVal c2 As Complex) As Complex
        Return New Complex(c1.Re - c2.Re, c1.Im - c2.Im)
    End Operator
    Public Shared Operator =(ByVal c1 As Complex, ByVal c2 As Complex) As Boolean
        Return (c1.Re = c2.Re) AndAlso (c1.Im = c2.Im)
    End Operator
    Public Shared Operator <>(ByVal c1 As Complex, ByVal c2 As Complex) As Boolean
        Return (c1.Re <> c2.Re) OrElse (c1.Im <> c2.Im)
    End Operator
    Public Shared Operator -(ByVal c1 As Complex) As Complex
        Return New Complex(c1.Im, c1.Re)
    End Operator
    Public Shared Narrowing Operator CType(ByVal c1 As Complex) As Double
        Return System.Math.Sqrt(c1.Re * c1.Re + c1.Im * c1.Im)
    End Operator
End Class

3 + 7i
-1 + 1i
-10 + 11i
False
True
4 + 1i
4.12310562561766

Complex Number

Public Class Tester

    Public Shared Sub Main
        Dim result As New System.Text.StringBuilder
        Dim a As ComplexNumber
        Dim b As ComplexNumber
        Dim c As ComplexNumber
        a = New ComplexNumber(3, 4)
        b = New ComplexNumber(5, -2)
        c = a + b
        result.AppendLine("Complex Numbers")
        result.AppendLine("a = " & a.ToString())
        result.AppendLine("b = " & b.ToString())
        " ----- Addition.
        c = a + b
        result.AppendLine("a + b = " & c.ToString())
        " ----- Subtraction.
        c = a - b
        result.AppendLine("a - b = " & c.ToString())
        " ----- Multiplication.
        c = a * b
        result.AppendLine("a * b = " & c.ToString())
        " ----- Division.
        c = a / b
        result.AppendLine("a / b = " & c.ToString())
        " ----- Addition as assignment.
        a += b
        result.AppendLine("a += b ... a = " & a.ToString())
        Console.WriteLine(result.ToString())
    End Sub
    
End Class
Structure ComplexNumber
    Public Real As Double
    Public Imaginary As Double
    Public Sub New(ByVal realPart As Double, ByVal imaginaryPart As Double)
        Me.Real = realPart
        Me.Imaginary = imaginaryPart
    End Sub
    Public Sub New(ByVal sourceNumber As ComplexNumber)
        Me.Real = sourceNumber.Real
        Me.Imaginary = sourceNumber.Imaginary
    End Sub
    Public Overrides Function ToString() As String
        Return Real & "+" & Imaginary & "i"
    End Function
    Public Shared Operator +(ByVal a As ComplexNumber, _
            ByVal b As ComplexNumber) As ComplexNumber
        Return New ComplexNumber(a.Real + b.Real, a.Imaginary + b.Imaginary)
    End Operator
    Public Shared Operator -(ByVal a As ComplexNumber, _
            ByVal b As ComplexNumber) As ComplexNumber
        Return New ComplexNumber(a.Real - b.Real, a.Imaginary - b.Imaginary)
    End Operator
    Public Shared Operator *(ByVal a As ComplexNumber, _
            ByVal b As ComplexNumber) As ComplexNumber
        Return New ComplexNumber(a.Real * b.Real - a.Imaginary * b.Imaginary, _
            a.Real * b.Imaginary + a.Imaginary * b.Real)
    End Operator
    Public Shared Operator /(ByVal a As ComplexNumber, _
            ByVal b As ComplexNumber) As ComplexNumber
        Return a * Reciprocal(b)
    End Operator
    Public Shared Function Reciprocal(ByVal a As ComplexNumber) As ComplexNumber
        Dim divisor As Double
        divisor = a.Real * a.Real + a.Imaginary * a.Imaginary
        If (divisor = 0.0#) Then Throw New DivideByZeroException
        Return New ComplexNumber(a.Real / divisor, -a.Imaginary / divisor)
    End Function
End Structure

Complex Numbers
a = 3+4i
b = 5+-2i
a + b = 8+2i
a - b = -2+6i
a * b = 23+14i
a / b = 0.241379310344828+0.896551724137931i
a += b ... a = 8+2i