If - and - - -1 then - -1- - equals

The correct option is C 1Given |α β1 α̅β̅ nbsp; | = |(α β)β̅β (1 α̅β̅ ̅)̅ nbsp; | = | α β | | β̅ | | β̅ α̅ | nbsp; ...(∵ββ̅ nbs ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

If α≠β and ...

Question

If $α \neq β$ and $| β | = 1$ then $∣ ∣ ∣ \frac{α - β}{1 - ¯ α β} ∣ ∣ ∣$ equals

-1

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None of these

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Solution

The correct option is C 1
Given $∣ ∣ ∣ \frac{α - β}{1 - ¯ α β} ∣ ∣ ∣$
$= ∣ ∣ ∣ ∣ \frac{(α - β) ¯ β}{β (1 - ¯ α β)} ∣ ∣ ∣ ∣$
$= \frac{| α - β | ∣ ∣ ¯ β ∣ ∣}{∣ ∣ ¯ β - ¯ α ∣ ∣} . . . (∵ β ¯ β = {∣ ∣ ¯ β ∣ ∣}^{2}) = ∣ ∣ β^{2} ∣ ∣ = 1)$
$= \frac{| α - β | | β |}{∣ ∣ ¯ ¯¯¯¯¯¯¯¯¯¯¯ ¯ β - α ∣ ∣}$
$= \frac{| α - β |}{| β - α |} (∵ | ¯ z | = | z |) = 1$

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If α≠β and |β|=1 then ∣∣∣α−β1−¯αβ∣∣∣ equals

If $α \neq β$ and $| β | = 1$ then $∣ ∣ ∣ \frac{α - β}{1 - ¯ α β} ∣ ∣ ∣$ equals