JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 August 2021, Shift 1, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

Let

z=\frac{1-i\sqrt{3}}{2}

i=\sqrt{-1}

. Then the value of

21+\left(z+\frac{1}{z}\right)^3+\left(z^2+\frac{1}{z^2}\right)^3+\left(z^3+\frac{1}{z^3}\right)^3+\ldots+\left(z^{21}+\frac{1}{z^{21}}\right)^3

is __________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Roots of Unity
Idea tested: De Moivre's Theorem

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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.