If (z-α/z+α) (α∈ R) is a purely imaginary number and |z| = 2, then a value of α is :

Question

If (z-α/z+α) (α∈ R) is a purely imaginary number and |z| = 2, then a value of α is : (A) 1 (B) 2 (C) √2 (D) (1/2)

Tardigrade Admin · Accepted Answer

(z-α/z+α) + ( barz -α/ barz +α) = 0 z barz+zα -α barz -α2 +z bar z - zα + barz α-α2 = 0 |z|2 = α2 , a = ±2

Q. If $\frac{z - α}{z + α} (α \in R)$ is a purely imaginary number and $∣ z ∣ = 2$ , then a value of $α$ is :