A) 0
B) 1
C) 1
D) 2
Correct Answer: C
Solution :
Given, \[|\beta |=1\Rightarrow |\beta {{|}^{2}}=1\Rightarrow \beta \overline{\beta }=1\] \[\therefore \] \[\left| \frac{\beta -\alpha }{1-\alpha \overline{\beta }} \right|=\left| \frac{\beta -\alpha }{\beta \overline{\beta }-\overline{\alpha }\beta } \right|\] \[=\left| \frac{\beta -\alpha }{\beta (\overline{\beta }-\overline{\alpha })} \right|\] \[=\frac{1}{|\beta |}\left| \frac{\beta -\alpha }{\overline{\beta }-\overline{\alpha }} \right|\] \[=\frac{1}{|\beta |}=1\] \[[\because |z|=|\overline{z}|]\]
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