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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

Let O be the origin and A be the point z1=1+2iz_1 = 1 + 2i. If B is the point z2z_2, Re(z2)<0\mathrm{Re}(z_2) < 0, such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true ?
  1. (1)arg⁡ z2=π−tan⁡−13\arg\ z_2 = \pi - \tan^{-1} 3
  2. (2)arg⁡ (z1−2z2)=−tan⁡−143\arg\ (z_1 - 2z_2) = -\tan^{-1}\frac{4}{3}
  3. (3)∣z2∣=10\left|z_2\right| = \sqrt{10}
  4. (4)∣2z1−z2∣=5\left|2z_1 - z_2\right| = 5Official answer

Official answer

Option 4

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Complex Numbers - Polar Form
Idea tested
Coni Method (Rotation Theorem)

Same topic in other shifts

All Complex Numbers - Polar Form questions
  1. 2 Apr 2026, Shift 2 · Q2Let the circles C1:∣z∣=rC_1: |z| = r and C2:∣z−3−4i∣=5,z∈CeC_2: |z - 3 - 4i| = 5, z \in \mathbb{C}_e be such that C2C_2 lies within C1C_1. If z1z_1 moves on…MediumSingle correct
  2. 4 Apr 2026, Shift 1 · Q3Let zz be a complex number such that ∣z+2∣=∣z−2∣|z+2|=|z-2| and arg⁡(z+3z−i)=π4\arg\left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}. Then ∣z∣2|z|^2 is equal to:MediumSingle correct
  3. 2 Apr 2025, Shift 1 · Q2Let zz be a complex number such that ∣z∣=1|z|=1. If 2+k2zk+zˉ=kz\frac{2+k^2z}{k+\bar{z}}=kz, k∈Rk\in\mathbf{R}, then the maximum distance of k+ik2k+ik^2…HardSingle correct
  4. 7 Apr 2025, Shift 1 · Q2Among the statements (S1) : The set {z∈C−{−i}:∣z∣=1\{z \in \mathbb{C} - \{-i\} : |z| = 1 and z−iz+i\frac{z-i}{z+i} is purely real}\} contains exactly two…MediumTwo statements
  5. 4 Apr 2024, Shift 1 · Q2Let α\alpha and β\beta be the sum and the product of all the non-zero solutions of the equation (zˉ)2+∣z∣=0(\bar{z})^2+|z|=0, z∈Cz \in C. Then…MediumSingle correct
  6. 5 Apr 2024, Shift 1 · Q2Consider the following two statements : Statement I : For any two non-zero complex numbers z1,z2z_1, z_2,…HardTwo 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.