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Let $a$ and $b$ be complex numbers with modulus $< 1$. How can I prove that $\left | \frac{a-b}{1-\bar{a}b} \right |<1$ ? Thank you

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    Is it homework? What did you try? Where are you stuck?2012-01-11
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    Not exactly homework. It is an oral question given at the entry test to the French school Ecole Polytechnique.2012-01-11

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