A) 0
B) \[\frac{3}{2}\]
C) \[\frac{1}{2}\]
D) 1
E) 2
Correct Answer: D
Solution :
\[\alpha \]and\[\beta \]are different complex numbers and \[|\beta |=1\] \[\left| \frac{\beta -\alpha }{1-\overline{\alpha }\beta } \right|=\frac{|\beta -\alpha |}{|1-\overline{\alpha }\beta |}\le \frac{|\beta -\alpha |}{|1-|\overline{\alpha }||\beta |}\] \[=\frac{1-|\alpha |}{1-|\alpha |}=1\] \[(\because |\overline{\alpha }|=|\alpha |)\]
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