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'(c) 2002 - 2004 by - Chillers of Entropy

'-> If the comments below look garbled then change font to COURIER NEW

' , ,

' / \/ \

' (/ //_ \_

' .-._ \|| . \

' \ '-._ _,:__.-"/---\_ \

' ______/___ '. .--------------------'~-'--.)__( , )\ \

'`'--.___ _\ / | ComplexArithmetic ,' \)|\ `\|

' /_.-' _\ \ _:,_ " || (

' .'__ _.' \'-/,`-~` |/

' '. ___.> /=,| 27/3/2002 - Riley T. Perry |

' / .-'/_ ) '---------------------------------'

' )' ( /(/ Riley@deliverance.com.au

' \\ "

' '=='

'

' *--------------------------------------------------------*

' * Varoius functions on complex numbers. *

' *--------------------------------------------------------*

Option Explicit

'**** Constants ****

Private Const CONSTANT_e As Double = 2.718281828

' .---.

' / . \

' |\_/| |

' | | /|

' .--------------------------------------------' |

' / .-. Multiply() |

' | / \ ---------- |

' | |\_. | Multiplies 2 complex numbers |

' |\| | /| /

' | `---' |--------------------------------------'

' \ | Parameters:

' \ / 1.>> SetType - The type of set to generate

' `---' 2.>> z1 - Multiplicand

' 3.>> z2 - Multiplier

'

' Returns:

' 1.<< Result (z1 * z2)

'

Public Function Multiply(ByVal z1 As CLASS_ComplexNumber, ByVal z2 As CLASS_ComplexNumber) As CLASS_ComplexNumber

'*------------------------------------------*

'* Multiply the 2 numbers *

'*------------------------------------------*

Dim dummy As New CLASS_ComplexNumber

dummy.x = (z1.x * z2.x) - (z1.y * z2.y)

dummy.y = (z1.x * z2.y) + (z2.x * z1.y)

'*------------------------------------------*

'* Clean up *

'*------------------------------------------*

Set Multiply = dummy

Set dummy = Nothing

End Function

' .---.

' / . \

' |\_/| |

' | | /|

' .--------------------------------------------' |

' / .-. Magnitude() |

' | / \ ----------- |

' | |\_. | Calculate magnitude of a complex no. |

' |\| | /| /

' | `---' |--------------------------------------'

' \ | Parameters:

' \ / 1.>> z - Complex number as argument

' `---'

' Returns:

' 1.<< Magnitude of argument

'

Public Function Magnitude(ByVal z As CLASS_ComplexNumber) As Double

'*------------------------------------------*

'* Calculate the Magnitude *

'*------------------------------------------*

Magnitude = Sqr((z.x * z.x) + (z.y * z.y))

End Function

' .---.

' / . \

' |\_/| |

' | | /|

' .--------------------------------------------' |

' / .-. Add() |

' | / \ ----- |

' | |\_. | Adds 2 complex numbers |

' |\| | /| /

' | `---' |--------------------------------------'

' \ | Parameters:

' \ / 1.>> z1 - Addend

' `---' 2.>> z2 - Augend

'

' Returns:

' 1.<< Sum of z1 and z2

'

Public Function Add(ByVal z1 As CLASS_ComplexNumber, ByVal z2 As CLASS_ComplexNumber) As CLASS_ComplexNumber

'*------------------------------------------*

'* Add the 2 numbers *

'*------------------------------------------*

Dim dummy As New CLASS_ComplexNumber

dummy.x = z1.x + z2.x

dummy.y = z1.y + z2.y

'*------------------------------------------*

'* Clean up *

'*------------------------------------------*

Set Add = dummy

Set dummy = Nothing

End Function

' .---.

' / . \

' |\_/| |

' | | /|

' .--------------------------------------------' |

' / .-. eToz() |

' | / \ ------ |

' | |\_. | Calculate e^z |

' |\| | /| /

' | `---' |--------------------------------------'

' \ | Parameters:

' \ / 1.>> z - Complex number as exponent

' `---'

' Returns:

' 1.<< Result of e^z

'

Public Function eToz(ByVal z As CLASS_ComplexNumber) As CLASS_ComplexNumber

'*------------------------------------------*

'* Calculate e^z *

'*------------------------------------------*

Dim dummy As New CLASS_ComplexNumber

'**** e^(a + bi) = e^a * cos(b) + e^a * sin(b) ****

dummy.x = (Exp(z.x)) * (Cos(z.y))

dummy.y = (Exp(z.x)) * (Sin(z.y))

'*------------------------------------------*

'* Clean up *

'*------------------------------------------*

Set eToz = dummy

Set dummy = Nothing

End Function

' .---.

' / . \

' |\_/| |

' | | /|

' .--------------------------------------------' |

' / .-. DegToRad() |

' | / \ ---------- |

' | |\_. | Convert Degrees to Rads |

' |\| | /| /

' | `---' |--------------------------------------'

' \ | Parameters:

' \ / 1.>> Degrees - number of degrees

' `---'

' Returns:

' 1.<< Degrees as Rads

'

Public Function DegToRad(ByVal Degrees As Double) As Double

'*------------------------------------------*

'* Convert to Radians *

'*------------------------------------------*

DegToRad = Degrees / 180 * 3.141592654

End Function

' .---.

' / . \

' |\_/| |

' | | /|

' .--------------------------------------------' |

' / .-. SinZ() |

' | / \ ------ |

' | |\_. | Calculate Sin(z) |

' |\| | /| /

' | `---' |--------------------------------------'

' \ | Parameters:

' \ / 1.>> z - Complex number as parameter

' `---'

' Returns:

' 1.<< Result of Sin(z)

'

Public Function SinZ(ByVal z As CLASS_ComplexNumber) As CLASS_ComplexNumber

'*------------------------------------------*

'* Calculate Sin(z) *

'*------------------------------------------*

Dim dummy As New CLASS_ComplexNumber

'**** sin(a + bi) = sin(x)cosh(y) + i*cos(x)sinh(y) ****

dummy.x = (Sin(z.x) * ((Exp(z.y) + Exp(-z.y)) / 2))

dummy.y = (Cos(z.x) * ((Exp(z.y) - Exp(-z.y)) / 2))

'*------------------------------------------*

'* Clean up *

'*------------------------------------------*

Set SinZ = dummy

Set dummy = Nothing

End Function