JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 September 2020, Shift 2, Maths Q53

Question 53 of 75 in this shift, Maths question 3 of 25.

The imaginary part of

\left(3+2\sqrt{-54}\right)^{1/2}-\left(3-2\sqrt{-54}\right)^{1/2}

can be :

(1) $6$
(2) $\sqrt{6}$
(3) $-2\sqrt{6}$ Official answer
(4) $-\sqrt{6}$

Official answer

Option 3

NTA final key (Sep 2020).

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Square Root via Polar Form

Same topic in other shifts

All Complex Numbers - Polar Form questions

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4 Apr 2024, Shift 1 · Q2Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\bar{z})^2+|z|=0$ , $z \in C$ . Then…MediumSingle correct
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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.