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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceTwo statementsMediumCalculation

JEE Main 30 July 2022, Shift 2, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

Let z1=1+2iz_1 = 1 + 2i, z2=2+iz_2 = 2 + i, 1z1+1z2=6w\frac{1}{z_1}+\frac{1}{z_2}=\frac{6}{w}, and z=iw2−w‾z = \frac{iw}{2-\overline{w}}. Consider the statements (S1\mathrm{S}_1) ∣z∣=517|z| = \frac{5}{\sqrt{17}} (S2\mathrm{S}_2) arg⁡(z)+arg⁡(w)=tan⁡−1(53)\arg(z) + \arg(w) = \tan^{-1}\left(\frac{5}{3}\right). Then
  1. (1)both (S1\mathrm{S}_1) and (S2\mathrm{S}_2) are wrong
  2. (2)only (S1\mathrm{S}_1) is correct
  3. (3)only (S2\mathrm{S}_2) is correct
  4. (4)both (S1\mathrm{S}_1) and (S2\mathrm{S}_2) are correctOfficial answer

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 13× in all
  1. 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
  2. 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
  3. 1 Feb 2024, Shift 1 · Q1Let S={z∈C:∣z−1∣=1S=\{z\in\mathbb{C}:|z-1|=1 and (2−1)(z+zˉ)−i(z−zˉ)=22}(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2\sqrt{2}\}. Let z1,z2∈Sz_1, z_2\in S be such that…HardSingle correct
  4. 29 Jan 2024, Shift 1 · Q3If z=12−2iz=\frac{1}{2}-2i is such that ∣z+1∣=αz+β(1+i)|z+1|=\alpha z+\beta(1+i), i=−1i=\sqrt{-1} and α,β∈R\alpha,\beta\in\mathbb{R}, then α+β\alpha+\beta is…EasySingle correct
  5. 30 Jan 2024, Shift 1 · Q2If z=x+iy, xy≠0z=x+iy,\ xy\neq0, satisfies the equation z2+izˉ=0z^2+i\bar{z}=0, then ∣z2∣|z^2| is equal to :MediumSingle correct
  6. 31 Jan 2024, Shift 1 · Q22If α\alpha denotes the number of solutions of ∣1−i∣x=2x|1-i|^x=2^x and β=(∣z∣arg⁡(z))\beta=\left(\frac{|z|}{\arg(z)}\right), where…MediumNumerical value
  7. 8 Apr 2023, Shift 1 · Q2If for z=α+iβz=\alpha+i\beta, ∣z+2∣=z+4(1+i)|z+2|=z+4(1+i), then α+β\alpha+\beta and αβ\alpha\beta are the roots of the equationMediumSingle correct
  8. 28 Jul 2022, Shift 2 · Q88Let z=a+ib, b≠0z=a+ib,\ b\neq 0 be complex numbers satisfying z2=zˉ⋅21−∣z∣z^2=\bar{z}\cdot 2^{1-|z|}. Then the least value of n∈Nn\in\mathbb{N}, such that…HardNumerical value

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.