Question

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

• A. 0
• B. ½
• C. 1
• D. 2

Answer 1

Answer: (C)

1

Answer 2

Sol. | b | = 1 Q | b|² = 1 Q $\beta\bar{\beta}$ = 1

$\left| \frac{\beta - \alpha}{1 - \bar{\alpha}\beta} \right| = \frac{|\beta - \alpha|}{|\beta|.|\overline{\beta - \alpha}|}$ = 1 (Q | z | = $|\bar{z}|$)