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JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 September 2020, Shift 2, Maths Q53

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

If

z_1

,

z_2

are complex numbers such that

\mathrm{Re}(z_1) = |z_1 - 1|

,

\mathrm{Re}(z_2) = |z_2 - 1|

and

\arg(z_1 - z_2) = \frac{\pi}{6}

, then

\mathrm{Im}(z_1 + z_2)

is equal to :

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

Official answer

Option 3

NTA final key (Sep 2020).

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Principal Argument Arithmetic

Same idea in other shifts

Asked 2× in all

25 Jun 2022, Shift 2 · Q3Let $z_1$ and $z_2$ be two complex numbers such that $\overline{z_1} = i\overline{z_2}$ and…MediumSingle correct

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.