JEE Main 2018MathematicsComplex NumberMediumMCQ

JEE Main 2018 — Complex Number Question with Solution

JEE Main 2018 (08 Apr)

Question

If α, β∈C are the distinct roots of the equation x2-x+1=0, then α101+β107 is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D1

Step-by-step explanation

x2-x+1=0

Roots are -ω, -ω2.

α101+β107=-ω101+-ω2107

=-ω2-ω ∵ω3=1

=-ω2+ω

=1 ∵1+ω+ω2=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.