JEE Main 2025 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 3 April 2025, Shift 1, Maths Q4

Question 4 of 75 in this shift, Maths question 4 of 25, Section A.

Let

z \in \mathbb{C}

be such that

\frac{z^2 + 3i}{z - 2 + i} = 2 + 3i

. Then the sum of all possible values of

z^2

(1) $19 - 2i$
(2) $-19 + 2i$
(3) $19 + 2i$
(4) $-19 - 2i$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Symmetric Functions

Same idea in other shifts

Asked 5× in all

2 Apr 2026, Shift 2 · Q1Let $\alpha, \beta$ be the roots of the equation $x^2 - 3x + r = 0$ , and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation…MediumSingle correct
31 Jan 2024, Shift 2 · Q3Let $z_1$ and $z_2$ be two complex numbers such that $z_1+z_2=5$ and $z_1^3+z_2^3=20+15i$ . Then, $|z_1^4+z_2^4|$ equals -HardSingle correct
24 Jun 2022, Shift 1 · Q7If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^2+\lambda x-1=0$ is 15, then…MediumSingle correct
29 Jun 2022, Shift 1 · Q8Let $\alpha$ and $\beta$ be the roots of the equation $x^2 + (2i - 1) = 0$ . Then, the value of $|\alpha^8 + \beta^8|$ is equal to :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.