JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 August 2021, Shift 2, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

(\sqrt{3}+i)^{100}=2^{99}(\mathrm{p}+i\mathrm{q})

, then p and q are roots of the equation :

(1) $x^2+(\sqrt{3}-1)x-\sqrt{3}=0$
(2) $x^2-(\sqrt{3}-1)x-\sqrt{3}=0$ Official answer
(3) $x^2-(\sqrt{3}+1)x+\sqrt{3}=0$
(4) $x^2+(\sqrt{3}+1)x+\sqrt{3}=0$

Official answer

Option 2

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: De Moivre's Theorem for Integer Powers

Same idea in other shifts

Asked 4× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.