If α and β are different complex numbers with | β | = 1, then (β-α/1- overline α β) is equal to

Question

If α and β are different complex numbers with | β | = 1, then (β-α/1- overline α β) is equal to (A) (1/2) (B) 1 (C) (1/3) (D) 2

Tardigrade Admin · Accepted Answer

Since, |β|=1 ∴ |β|2=β barβ=1 ∴ |(β-α/1- barα β)| =|(β-α/β barβ- barα β)| =(|β-α|/|β|| barβ- barα|) =(|β-α|/1 ⋅| overlineβ-α|) =1

Q. If $α$ and $β$ are different complex numbers with $∣ β ∣ = 1$ , then $\frac{β - α}{1 - α β}$ is equal to