QJEEM19Ma1ae3: JEE Main 2019 Mathematics - Class 11 JEEM19Ma1ae3 Solution: If is a purely imaginary number and

Question

Verified Solution • 2025–26 Session moderate

If

{{z - \alpha } \over {z + \alpha }}\left( {\alpha \in R} \right)

is a purely imaginary number and | z | = 2, then a value of

\alpha

is :

Accepted Answer

{{z - \alpha } \over {z + \alpha }} + {{\overline z - \alpha } \over {\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

{\left| z \right|^2} = {\alpha ^2},

a = \pm 2

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