JEE Main 2026 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 4 April 2026, Shift 2, Maths Q2

Question 2 of 75 in this shift, Maths question 2 of 25, Section A.

Let

S=\{z\in\mathbb{C}:z^2+4z+16=0\}

. Then

\sum_{z\in S}|z+\sqrt{3}\,i|^2

is equal to:

(1)42
(2)23
(3)27
(4)38Official answer

Official answer

Option 4

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Complex Conjugate Roots

Same idea in other shifts

Asked 4× in all

4 Apr 2026, Shift 2 · Q4If $\alpha=1$ and $\beta=1+i\sqrt{2}$ , where $i=\sqrt{-1}$ are two roots of the equation $x^3+ax^2+bx+c=0$ , $a,b,c\in\mathbb{R}$ , then…MediumSingle correct
31 Jan 2024, Shift 1 · Q7Let $a$ be the sum of all coefficients in the expansion of $(1-2x+2x^2)^{2023}(3-4x^2+2x^3)^{2024}$ and…HardSingle correct
8 Jan 2020, Shift 1 · Q52If the equation, $x^2+bx+45=0$ ( $b\in R$ ) has conjugate complex roots and they satisfy $|z+1|=2\sqrt{10}$ , then :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.