If - - are two non zero complex numbers and - is uni modular then the value of -1- is

The correct option is C 1 |β| = 1 ⇒ββ = 1 ⇒β = 1/β So | α β/1 αβ| = | α β |/| 1 α1/β| = | α β | /|β α | |β| = 1 ...

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Standard XI

Mathematics

Logarithms

If α, β are t...

Question

If $α, β$ are two non zero complex numbers and $β$ is uni modular then the value of $∣ ∣ \frac{α - β}{1 - ¯ ¯ ¯ α β} ∣ ∣$ is

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Solution

The correct option is B
1

$| β | = 1 \Rightarrow β ¯ ¯ ¯ β = 1 \Rightarrow β = \frac{1}{β}$

So $∣ ∣ \frac{α - β}{1 - ¯ ¯ ¯ α β} ∣ ∣ = \frac{| α - β |}{∣ ∣ ∣ 1 - α \frac{1}{β} ∣ ∣ ∣} = \frac{| α - β |}{| ¯ ¯ ¯ β - ¯ ¯ ¯ α |} | ¯ ¯ ¯ β | = 1$

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If α,β are two non zero complex numbers and β is uni modular then the value of ∣∣α−β1−¯¯¯αβ∣∣ is

The correct option is B 1 |β|=1 ⇒ β¯¯¯β=1 ⇒ β=1β So ∣∣α−β1−¯¯¯αβ∣∣=|α−β|∣∣∣1−α1β∣∣∣=|α−β||¯¯¯β−¯¯¯α||¯¯¯β|=1

If $α, β$ are two non zero complex numbers and $β$ is uni modular then the value of $∣ ∣ \frac{α - β}{1 - ¯ ¯ ¯ α β} ∣ ∣$ is

The correct option is B
1

$| β | = 1 \Rightarrow β ¯ ¯ ¯ β = 1 \Rightarrow β = \frac{1}{β}$

So $∣ ∣ \frac{α - β}{1 - ¯ ¯ ¯ α β} ∣ ∣ = \frac{| α - β |}{∣ ∣ ∣ 1 - α \frac{1}{β} ∣ ∣ ∣} = \frac{| α - β |}{| ¯ ¯ ¯ β - ¯ ¯ ¯ α |} | ¯ ¯ ¯ β | = 1$