If - - be any two complex numbers such that -1- -1- then which of the following may be true

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

and

β

are different complex numbers with

| β | = 1,

then the value of

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

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If α,β be any two complex numbers such that ∣∣α−β1−¯¯¯αβ∣∣=1, then which of the following may be true

The correct options are A |α|=1 B |β|=1 C α=eiθ,θϵR D β=eiθ,θϵRSimplifying, we get |α−β|=|1−¯α.β|Now if we consider α=βThen¯α.β=¯α.α=|α|2Now if we consider |α|=1Hence |α|2=1HenceLHS=RHS=0 if α=β and |α|=1Hence all of the above options are true.

If $α, β$ be any two complex numbers such that $∣ ∣ \frac{α - β}{1 - ¯ ¯ ¯ α β} ∣ ∣ = 1$ , then which of the following may be true