SuperStrict

Global a:String = "3:7"
Global b:String = "4:2"

Print "Add:         " + Add(a, b)
Print "Subtract:    " + Subtract(a, b)
Print "Multiply:    " + Multiply(a, b)
Print "Divide:      " + Divide(a, b)
Print "Exponentiate:" + Exponentiate(a, 2)
Print "Root:        " + Exponentiate(a, 1 / 2.0)
Print ""
Print "Argument:    " + Argument(b)
Print "Absolute:    " + CAbs(a)
Print "Complex Conjugate: " + CConjugate(a)



Function Re:Double(z:String)
   Return Double(Left(z, Instr(z, ":")))
End Function

Function Im:Double(z:String)
   Return Double(Right(z, Instr(z, ":") - 1))
End Function

Function Argument:Double(z:String)
   Return ATan2(Im(z), Re(z))
End Function

Function CAbs:Double(z:String)
   Local a:Double = re(z)
   Local b:Double = im(z)
   Return Sqr(a * a + b * b)
End Function

Function CConjugate:String(z:String)
   Return Re(z) + ":" + (-Im(z))
End Function

Function Add:String(z1:String, z2:String)
   Return (Re(z1) + Re(z2)) + ":" + (Im(z1) + Im(z2))
End Function

Function Subtract:String(z1:String, z2:String)
   Return (Re(z1) - Re(z2)) + ":" + (Im(z1) - Im(z2))
End Function

Function Multiply:String(z1:String, z2:String)
   Local a:Double = Re(z1)
   Local b:Double = Im(z1)
   Local c:Double = Re(z2)
   Local d:Double = Im(z2)
   Return (a * c - b * d) + ":" + (a * d + b * c)
End Function

Function Divide:String(z1:String, z2:String)
   Local a:Double = Re(z1)
   Local b:Double = Im(z1)
   Local c:Double = Re(z2)
   Local d:Double = Im(z2)
   Return ((a * c + b * d) / (c * c + d * d)) + ":" + ((b * c - a * d) / (c * c + d * d))
End Function

Function Exponentiate:String(z1:String, Exponent:Double)
   Local a:Double = Re(z1)
   Local b:Double = Im(z1)
   Local w:Double = ATan2(b, a) * exponent
   Local l:Double = Sqr(a * a + b * b) ^ exponent
   Return (Cos(w) * l) + ":" + (Sin(w) * l)
End Function

SuperStrict

Local a:CNum = New CNum
a.Is(3, 7)
Local b:CNum = New CNum
b.Is(4, 2)
Print a.re

Print "Add:         " + CNumToString(Add(a, b))
Print "Subtract:    " + CNumToString(Subtract(a, b))
Print "Multiply:    " + CNumToString(Multiply(a, b))
Print "Divide:      " + CNumToString(Divide(a, b))
Print "Exponentiate:" + CNumToString(Exponentiate(a, 2))
Print "Root:        " + CNumToString(Exponentiate(a, 1 / 2.0))
Print ""
Print "Argument:    " + Argument(b)
Print "Absolute:    " + CAbs(a)
Print "Complex Conjugate: " + CNumToString(CConjugate(a))



Type CNum
   Field re:Double
   Field im:Double
   
   Method Is(Re:Double, Im:Double)
      Self.Re = Re
      Self.Im = Im
   End Method
End Type


Function Argument:Double(z:CNum)
   Return ATan2(z.im, z.re)
End Function

Function CAbs:Double(z:CNum)
   Return Sqr(z.re * z.re + z.im * z.im)
End Function

Function CConjugate:CNum(z:CNum)
   z.im = -z.im
   Return z
End Function

Function Add:CNum(a:CNum, b:CNum)
   Local res:CNum
   res.re = a.re + b.re
   res.im = a.im + b.im
   Return res
End Function

Function Subtract:CNum(a:CNum, b:CNum)
   Local res:CNum
   res.re = a.re - b.re
   res.im = a.im - b.im
   Return res
End Function

Function Multiply:CNum(a:CNum, b:CNum)
   Local res:CNum
   res.re = a.re * b.re - a.im * b.im
   res.im = a.re * b.im + a.im * b.re
   Return res
End Function

Function Divide:CNum(a:CNum, b:CNum)
   Local res:CNum
   res.re = (a.re * b.re + a.im * b.im) / (b.re * b.re + b.im * b.im)
   res.im = (a.im * b.re - a.re * b.im) / (b.re * b.re + b.im * b.im)
   Return res
End Function

Function Exponentiate:CNum(z:CNum, Exponent:Double)
   Local res:CNum
   Local w:Double = ATan2(z.im, z.re) * Exponent
   Local l:Double = Sqr(z.re * z.re + z.im * z.im) ^ Exponent
   res.re = Cos(w) * l
   res.im = Sin(w) * l
   Return res
End Function

Function CNumToString:String(z:CNum)
   If z.im >= 0
      Return z.re + "+" + z.im + "i"
   Else
      Return z.re + "" + z.im + "i"
   End If
End Function