The set of all α R, for which w = (1 + (1 - 8α)z)/(1 - z) is purely imaginary number, for all z C satisfying |z| = 1 and Re z ≠ 1, is:

Complex Numbers and Quadratic Equations: JEE Main 2018 Mathematics question

JEE Main 2018 · 15 Apr, Morning shift · Q3150

JEE Main 201815 Apr, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

The set of all

\alpha

\in

R, for which w =

{{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}

is purely imaginary number, for all z

\in

C satisfying |z| = 1 and Re z

\ne

1, is :