JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2023, Shift 1, Maths Q2

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

If for

z=\alpha+i\beta

|z+2|=z+4(1+i)

, then

\alpha+\beta

and

\alpha\beta

are the roots of the equation

(1) $x^2+3x-4=0$
(2) $x^2+7x+12=0$ Official answer
(3) $x^2+2x-3=0$
(4) $x^2+x-12=0$

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
1 Feb 2024, Shift 1 · Q1Let $S=\{z\in\mathbb{C}:|z-1|=1$ and $(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2\sqrt{2}\}$ . Let $z_1, z_2\in S$ be such that…HardSingle 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
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.