If $\alpha$ and $\beta$ are different complex numbers with $|\beta| = 1\ then\ \left| \frac{\beta - \alpha}{1 - \overline{\alpha}\beta} \right|\$is equal to

Question

Dr. Abubacker · Accepted Answer

(c)
Given that, $|\beta| = 1$
$	herefore\ \ \left| \frac{\beta - \alpha}{1 - \overline{\alpha}\beta} ight| = \left| \frac{\beta - \alpha}{\beta\ \overline{\beta} - \overline{\alpha}\beta} ight|$
$= \ \left| \frac{\beta - \alpha}{\overline{\beta}(\overline{\beta} - \overline{\alpha})} ight| = \frac{1}{|\beta|}\left| \frac{\beta - \alpha}{\left( \overline{\beta} - \overline{\alpha} ight)} ight|$
$= \ \frac{1}{|\beta|} = 1\ \ (\because\left| \mathcal{z} ight| = \left| \overline{\mathcal{z}} ight|)$

Q. If $\alpha$ and $\beta$ are different complex numbers with $|\beta| = 1\ then\ \left| \frac{\beta - \alpha}{1 - \overline{\alpha}\beta} \right|\$is equal to

Explanation

Reviewed by Dr. Abubacker

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