Algebra> Sir please tell me question 8...............

Sir please tell me question 8..........................

Pushkar Kumar , 6 Years ago

Grade 12

1 Answers

Samyak Jain

Last Activity: 6 Years ago

$\alpha$ and $\beta$ are two distinct complex numbers with | $\beta$ | = 1 ...(1)

We know that z z(bar) = |z|² , so $\beta$ $\beta$ (bar) = | $\beta$ |² = 1 ...(2)

Also, | $\beta$ | = | $\beta$ (bar)| and | $\alpha$ | = | $\alpha$ (bar)| ...(2)

Now, |( $\beta$ – $\alpha$ )/(1 – $\alpha$ (bar) $\beta$ )| = | $\beta$ – $\alpha$ | / |1 – $\alpha$ (bar) $\beta$ | = | $\beta$ – $\alpha$ | / | $\beta$ $\beta$ (bar) – $\alpha$ (bar) $\beta$ | [from (2)]

= | $\beta$ – $\alpha$ | / | $\beta$ ( $\beta$ (bar) – $\alpha$ (bar))|

= | $\beta$ – $\alpha$ | / { | $\beta$ | | $\beta$ (bar) – $\alpha$ (bar)| }

= | $\beta$ – $\alpha$ | / { | $\beta$ | | $\beta$ – $\alpha$ |} = 1/| $\beta$ | [using (2)]

= 1. [from (1)]

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Algebra> Sir please tell me question 8...............

Sir please tell me question 8..........................

Pushkar Kumar , 6 Years ago

Samyak Jain

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