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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q3

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

Let z1z_1 and z2z_2 be two complex numbers such that z1‾=iz2‾\overline{z_1} = i\overline{z_2} and arg⁡(z1z2‾)=π\arg\left(\frac{z_1}{\overline{z_2}}\right) = \pi. Then
  1. (1)arg⁡z2=π4\arg z_2 = \frac{\pi}{4}
  2. (2)arg⁡z2=−3π4\arg z_2 = -\frac{3\pi}{4}
  3. (3)arg⁡z1=π4\arg z_1 = \frac{\pi}{4}Official answer
  4. (4)arg⁡z1=−3π4\arg z_1 = -\frac{3\pi}{4}

Official answer

Option 3

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Complex Numbers - Polar Form
Idea tested
Principal Argument Arithmetic

Same idea in other shifts

Asked 2× in all
  1. 3 Sep 2020, Shift 2 · Q53If z1z_1, z2z_2 are complex numbers such that Re(z1)=∣z1−1∣\mathrm{Re}(z_1) = |z_1 - 1|, Re(z2)=∣z2−1∣\mathrm{Re}(z_2) = |z_2 - 1| and…HardSingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.