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Friday, 9 October

JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 11 April 2023, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let w1w_1 be the point obtained by the rotation of z1=5+4iz_1 = 5 + 4i about the origin through a right angle in the anticlockwise direction, and w2w_2 be the point obtained by the rotation of z2=3+5iz_2 = 3 + 5i about the origin through a right angle in the clockwise direction. Then the principal argument of w1−w2w_1 - w_2 is equal to
  1. (1)π−tan⁡−1335\pi - \tan^{-1}\frac{33}{5}
  2. (2)−π+tan⁡−1335-\pi + \tan^{-1}\frac{33}{5}
  3. (3)π−tan⁡−189\pi - \tan^{-1}\frac{8}{9}Official answer
  4. (4)−π+tan⁡−189-\pi + \tan^{-1}\frac{8}{9}

Official answer

Option 3

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Complex Numbers - Polar Form
Idea tested
90-Degree Rotation via 'i'

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. 6 Apr 2024, Shift 2 · Q3If z1,z2z_1, z_2 are two distinct complex number such that ∣z1−2z212−z1z2ˉ∣=2\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2, thenHardSingle correct
  6. 8 Apr 2024, Shift 1 · Q2Let zz be a complex number such that ∣z+2∣=1|z+2|=1 and Im(z+1z+2)=15\mathrm{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}. Then the value of…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.