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MathGroup Archive 2004

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Question about composing a complex function.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49765] Question about composing a complex function.
  • From: gilmar.rodriguez at nwfwmd.state.fl.us (Gilmar Rodr?guez Pierluissi)
  • Date: Fri, 30 Jul 2004 06:02:17 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Mathematica Group:
Let |z-w|=r^2 be a circle with radius r and center w in the complex
plane C.
The function T(z) = w + (r^2/Conjugate(z)-Conjugate(w)) with w,z
Complex and r Real,
takes the interior of that circle to its exterior, and viceversa,
leaving the boundary of the circle fixed.
Also T(T(z)) = z, i.e. T(T(z)) acts like the identity function I(z)=z.
If I (refering to myself) define:
T[z_] := w + (r^2/(Conjugate(z)-Conjugate(w)))
and evaluate:
Simplify[T[T[z]]]
or:
Composition[T,T]
why can't Mathematica give the answer directly; namely, z ?
What I'm I missing?
Thank you for your help!


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