JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

\alpha

denotes the number of solutions of

|1-i|^x=2^x

and

\beta=\left(\frac{|z|}{\arg(z)}\right)

, where

z=\frac{\pi}{4}(1+i)^4\left[\frac{1-\sqrt{\pi}i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi}i}\right]

i=\sqrt{-1}

, then the distance of the point

(\alpha,\beta)

from the line

4x-3y=7

is ______

Official answer

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
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.