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 ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

If α and β are different complex numbers with = 1, then find.

If $α$ and $β$ are different complex numbers with $| β | = 1$ then find $∣ ∣ \frac{β - α}{1 - ¯ α β} ∣ ∣$
Here $α$ and $β$ are different complex numbers such that $| β | = 1$

Q. If

α, β

are the roots of

x^{2} + 3 x - 2 = 0

then

\frac{α + 1}{β} + \frac{β + 1}{α}

= ?

If α and β are different complex numbers with = 1, then find.

Q. If

α, β, γ

are roots of

x^{3} + 4 x + 1 = 0

, then

(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1}

equals

Join BYJU'S Learning Program

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