+1 vote
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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)$$1\over2$$

reopened | 62 views

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