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Find all linear fractional transformation that maps {$z:Im(z)>0$} to {$w:|w|<1$}

I don't know anything about this.. Can you help me?

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Hint: Find one, call it $T$. Suppose there is another. Call it $S$. Then $TS^{-1}$ maps the disc conformally to itself, hence has a very precise form. Use your knowledge of this form and the inverse of $T$ to find a general form for $S$.

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You need to use Bilinear Transformations.

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    $\begingroup$ thx 4 the link. $\endgroup$ – user114952 Jan 28 '14 at 6:33
  • $\begingroup$ @user114952: You are wecome. $\endgroup$ – Mhenni Benghorbal Jan 28 '14 at 6:34

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