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Let \(\alpha\) and \(\beta\) be complex numbers such that \(|\beta| = 1\) and \(\overline{\alpha} \beta \neq 1\). Find the maximum value of \(\left| \frac{\beta - \alpha}{1 - \overline{\alpha} \beta} \right|.\)

 Dec 31, 2022
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By the maximum modulus principle, the answer is 4.

 Dec 31, 2022

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