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 5× in all

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
9 Jan 2020, Shift 2 · Q53If $z$ be a complex number satisfying $|\mathrm{Re}(z)|+|\mathrm{Im}(z)|=4$ , then $|z|$ cannot be :MediumSingle correct
6 Sep 2020, Shift 2 · Q53Let $z=x+iy$ be a non-zero complex number such that $z^2=i|z|^2$ , where $i=\sqrt{-1}$ , then $z$ lies on the :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 42 of the 174 JEE Main shifts held from 2017 to 2026.