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

A)1

B)2

C)\(\sqrt2\)

D)\(1\over2\)

The correct answer is B) 2

Explanation ::

\(\dfrac { { z }-\alpha }{ { z }+\alpha } +\dfrac { \overline { { z } } -\alpha }{ \overline { { z } } +\alpha } =0\)

\(z \overline { z } + z \alpha - \alpha \overline { z } - \alpha ^ { 2 } + z \overline { z } - z \alpha + \overline { z } \alpha - \alpha ^ { 2 } = 0\)

\(|{ z }| ^{ { 2 } } =\alpha ^{ { 2 } },\quad { \alpha }=\pm 2 \)