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

Question

Dr. Abubacker · Accepted Answer

(d)
Given, $\alpha$ and $\beta$ are different complex numbers and
$|\beta| = 1$
$	herefore\ \ \ \ \ \left| \frac{\beta - \alpha}{1 - \overline{\alpha}\beta} ight| = \frac{|\beta - \alpha|}{|\beta\overline{\beta} - \overline{\alpha}\beta|} = \frac{|\beta - \alpha|}{|\beta||\overline{\beta} - \overline{\alpha}|} = 1\ \$

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

Explanation

Reviewed by Dr. Abubacker

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