Question

Complex number JEE Main 2021 questions PYQ

Answer 1

Complex number JEE Main 2021 questions PYQ 

Q1)Let a complex number be w = 1 – √3i . Let another complex number z be such that |zw| = 1 and arg(z) – arg(w) = \(\frac{\pi}2\) . Then the area of the triangle with vertices origin, z and w is equal to :

(1) 4

(2) \(\frac 12\)

(3) \(\frac 14\)

(4) 2

Q2) If the equation a|z|² + \(\overline{\overline\alpha z+\alpha\overline z}\) + d = 0 represents a circle where a, d are real constants then which of the following condition is correct ?

(1) |α|²- ad ≠ 0

(2) |α|² - ad > 0 and a ∈ R - {0}

(3) |α|² - ad ≥ 0 and a ∈ R

(4) α = 0, a, d∈ R⁺

Q3) Let S₁, S₂ and S₃ be three sets defined as

\(S_1=\{z \in \mathbb C:|z-1|\leq \sqrt{2}\}\)

\(S_2=\{z \in \mathbb C:\text{Re} \big((1-i)z\big)\geq 1\}\)

\(S_3=\{z \in \mathbb C:\text{Im}(z)\leq 1\}\)

Then the set \(S_1\cap S_2\cap S_3\)

(1) Is a singleton

(2) Has exactly two elements

(3) Has infinitely many elements

(4) Has exactly three elements

Q4) The area of the triangle with vertices A(z), B(iz) and C (z + iz) is :

(1) 1

(2) \(\frac{1}{2}|z|^2\)

(3) \(\frac{1}{2}\)

(4) \(\frac{1}{2}|z+iz|^2\)

Q5) The least value of |z| where z is complex number which satisfies the inequality

exp \(\bigg(\frac{(|z|+3)(|z|-1)}{\big||z|+1 \big|}log_{e^2}\bigg)\) \(\geq log_\sqrt{2}\big|5\sqrt{7}+9i \big|,\)

\(i=\sqrt{-1},\) is equal to:

(1) 3

(2) \(\sqrt{5}\)

(3) 2

(4) 8