JEE Main 2018MathematicsComplex NumberHardMCQ

JEE Main 2018 — Complex Number Question with Solution

JEE Main 2018 (15 Apr)

Question

The set of all α∈R, for which w=1+1-8αz1-z is a purely imaginary number, for all z∈C satisfying z=1 and Rez≠1, is :

Choose an option

Show full solutionCorrect option: A
Correct answer
A0

Step-by-step explanation

For w to be purely imaginary, 1+1-8αz1-z+1+1-8αz¯1-z¯=0

⇒1-z¯+1-8αz-1-8α+1-z+1-8αz¯-1-8α=0

⇒2-z+z¯+1-8αz+z¯-2+16α=0

⇒8αz+z¯=16α

⇒z+z¯=2 or α=0

For all z∈C, we have α=0.

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About this question

This is a previous-year question from JEE Main 2018, covering the Complex Number chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.