JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 1 February 2024, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

Let

S=\{z\in\mathbb{C}:|z-1|=1

and

(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2\sqrt{2}\}

. Let

z_1, z_2\in S

be such that

|z_1|=\max_{z\in S}|z|

and

|z_2|=\min_{z\in S}|z|

. Then

\left|\sqrt{2}z_1-z_2\right|^2

equals :

(1)1
(2)2Official answer
(3)3
(4)4

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 13× in all

5 Apr 2024, Shift 1 · Q2Consider the following two statements : Statement I : For any two non-zero complex numbers $z_1, z_2$ ,…HardTwo statements
6 Apr 2024, Shift 2 · Q3If $z_1, z_2$ are two distinct complex number such that $\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2$ , thenHardSingle correct
29 Jan 2024, Shift 1 · Q3If $z=\frac{1}{2}-2i$ is such that $|z+1|=\alpha z+\beta(1+i)$ , $i=\sqrt{-1}$ and $\alpha,\beta\in\mathbb{R}$ , then $\alpha+\beta$ is…EasySingle correct
30 Jan 2024, Shift 1 · Q2If $z=x+iy,\ xy\neq0$ , satisfies the equation $z^2+i\bar{z}=0$ , then $|z^2|$ is equal to :MediumSingle correct
31 Jan 2024, Shift 1 · Q22If $\alpha$ denotes the number of solutions of $|1-i|^x=2^x$ and $\beta=\left(\frac{|z|}{\arg(z)}\right)$ , where…MediumNumerical value
8 Apr 2023, Shift 1 · Q2If for $z=\alpha+i\beta$ , $|z+2|=z+4(1+i)$ , then $\alpha+\beta$ and $\alpha\beta$ are the roots of the equationMediumSingle correct
28 Jul 2022, Shift 2 · Q88Let $z=a+ib,\ b\neq 0$ be complex numbers satisfying $z^2=\bar{z}\cdot 2^{1-|z|}$ . Then the least value of $n\in\mathbb{N}$ , such that…HardNumerical value
30 Jul 2022, Shift 2 · Q62Let $z_1 = 1 + 2i$ , $z_2 = 2 + i$ , $\frac{1}{z_1}+\frac{1}{z_2}=\frac{6}{w}$ , and $z = \frac{iw}{2-\overline{w}}$ . Consider the statements…MediumTwo statements

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.