JEE Main 2024 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 29 January 2024, Shift 1, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

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 equal to

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

Official answer

Option 3

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
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
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.