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!