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Can anyone spot a complex number $z\in\mathbb C$ such that for $a,b\in \mathbb C$ and $f(w)={w-z\over {w-\overline{z}}}$, we have ${f(a)-f(b)\over {1-\overline{f(a)}f(b)}}={b-a\over {b-\overline{a}}}$. I have been staring at this for some time now...

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    Maybe from $f(w^*) = \left(\frac{1}{f(w)}\right)^*$?2012-02-24

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