If a and β are different complex numbers with |β|=1, then β−α1−α¯β is equal to

|β|=1 ∴ |β|2=ββ¯=1∴ L.H.S. =β−αββ¯−α¯β=|β−α||β|β¯−α¯ =|β−α|1.|β−α¯|=1 ∵ z¯=z

If a and β are different complex numbers with |β|=1, then β−α1−α¯β is equal to

|β|=1 ∴ |β|2=ββ¯=1∴ L.H.S. =β−αββ¯−α¯β=|β−α||β|β¯−α¯ =|β−α|1.|β−α¯|=1 ∵ z¯=z

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If $a$ and $β$ are different complex numbers with $| β | = 1$ , then $|\frac{β - α}{1 - \bar{α} β}|$ is equal to

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Detailed Solution

$\begin{array}{l} | β | = 1 ∴ | β |^{2} = β \bar{β} = 1 \\ ∴ L.H.S. = |\frac{β - α}{β \bar{β} - \bar{α} β}| = \frac{| β - α |}{| β | \bar{β} - \bar{α}} \\ = \frac{| β - α |}{1 . | \bar{β - α} |} = 1 ∵ \bar{z} = z \end{array}$