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Question: If a, b are two different complex number such that \|a\| = 1, \|b\| = 1 then the expression \(\left|...

If a, b are two different complex number such that |a| = 1, |b| = 1 then the expression ∣β−α1−αˉβ∣\left| \frac{\beta - \alpha}{1 - \bar{\alpha}\beta} \right| equals :

A

12\frac{1}{2}

B

1

C

2

D

None of these

Answer

1

Explanation

Solution

Sol. ∣β−α∣∣ββˉ−αˉβ∣\frac{|\beta - \alpha|}{|\beta\bar{\beta} - \bar{\alpha}\beta|}= ∣β−α∣∣β∣∣βˉ−αˉ∣\frac{|\beta - \alpha|}{|\beta||\bar{\beta} - \bar{\alpha}|}=∣β−α∣∣β∣∣β−α‾∣\frac{|\beta - \alpha|}{|\beta||\overline{\beta - \alpha}|} = 1