If - and - are different complex numbers with -1 then find -1- Here - and - are different complex numbers such that -1

| β α/1 α̅β |^2 = | β α/1 α̅β | [ β α/1 α̅β ] [∵ |z|^2=zz̅] = [ β α/1 α̅β ] [ β̅ α̅/1 αβ ] =ββ̅ βα̅ αβ̅+αα̅/1 α̅β αβ̅+αα̅ββ̅ =|β |^2 α̅β αβ̅+|α |^2/1 α̅ ...

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Byju's Answer

Standard XI

Statistics

Covariance

If α and β ar...

Question

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 $| β | = 1$

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Solution

${∣ ∣ \frac{β - α}{1 - ¯ α β} ∣ ∣}^{2}$

$= ∣ ∣ \frac{β - α}{1 - ¯ α β} ∣ ∣ [\frac{¯ ¯¯¯¯¯¯¯ ¯ β - α}{¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 1 - ¯ α β}] [∵ | z |^{2} = z ¯ z]$

$= [\frac{β - α}{1 - ¯ α β}] [\frac{¯ β - ¯ α}{1 - α β}]$

$= \frac{β ¯ β - β ¯ α - α ¯ β + α ¯ α}{1 - ¯ α β - α ¯ β + α ¯ α β ¯ β}$

$= \frac{| β |^{2} - ¯ α β - α ¯ β + | α |^{2}}{1 - ¯ α β - α ¯ β + | α |^{2} | β |^{2}}$

$= \frac{1 - ¯ α β - α ¯ β + | α |^{2}}{1 - ¯ α β - ¯ α β + | α |^{2}} = 1$

$∴ ∣ ∣ \frac{β - α}{1 - α β} ∣ ∣ = 1$

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

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α

and

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are different complex numbers with

| β | = 1,

then the value of

∣ ∣ ∣ \frac{β - α}{1 - ¯ ¯¯ ¯ α β} ∣ ∣ ∣

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

Q. If

α, β

are different complex numbers with

| β | = 1

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∣ ∣ ∣ \frac{¯ ¯¯ ¯ α - β}{1 - α β} ∣ ∣ ∣ =

Q. If

α

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are two different complex numbers such that

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∣ ∣ ∣ \frac{β - α}{1 - ¯ α β} ∣ ∣ ∣

equals :

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If α and β are different complex numbers with |β|=1 then find ∣∣β−α1−¯αβ∣∣ Here α and β are different complex numbers such that |β|=1

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 $| β | = 1$