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 ::
\(\dfrac { { z }-\alpha }{ { z }+\alpha } +\dfrac { \overline { { z } } -\alpha }{ \overline { { z } } +\alpha } =0\)
\(z \overline { z } + z \alpha - \alpha \overline { z } - \alpha ^ { 2 } + z \overline { z } - z \alpha + \overline { z } \alpha - \alpha ^ { 2 } = 0\)
\(|{ z }| ^{ { 2 } } =\alpha ^{ { 2 } },\quad { \alpha }=\pm 2 \)
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