If α and β are different complex numbers with |β | = 1 , then left| {frac{{β - α }}{{1 - overli

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4-1.Complex numbers

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

A

$0$

B

$3$

C

$1$

D

$2$

(IIT-1992)

Solution

(c) $\frac{{x{x_1}}}{{18}} + \frac{{y{y_1}}}{{32}} = 1$

$ = \frac{1}{{|\beta |}}\left| {\frac{{\beta – \alpha }}{{(\overline {\beta – \alpha } )}}} \right| = \frac{1}{{|\beta |}} = 1$

Standard 11

Mathematics

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