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

Step-by-step solution

If a complex number is purely imaginary, then it must be equal to negative of its conjugate. ⇒ z - α z + α = - z - α z + α ⇒ z - α z + α = - z - - α z - + α ⇒ z - α z - + α = z + α z - - α ⇒   z z - + α z - α z - - α 2 = - z z - - α z + α z - - α 2 ⇒ z 2 = α 2 ⇒ α 2 = 4   ∵ z = 2 ⇒ α = ± 2