Mathematics · 2023
JEE Main · 11 April 2023, Shift 1 · Q14
Let w_1 be the point obtained by the rotation of z_1=5+4 i about the origin through a right angle in the anticlockwise direction, and w_2 be the…
Let $\displaystyle w_1$ be the point obtained by the rotation of $\displaystyle z_1=5+4 i$ about the origin through a right angle in the anticlockwise direction, and $\displaystyle w_2$ be the point obtained by the rotation of $\displaystyle z_2=3+5 i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $\displaystyle w_1-w_2$ is equal to
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle \pi-\tan ^{-1} \frac{8}{9}$
More from Complex Numbers
- Let A={θ ∈(0,2 π): (1+2 i sin θ)/(1-i sin θ). is purely imaginary }. Then the sum of the elements in A is2023
- Let S={z: 3 ≤|2 z-3(1+i)| ≤ 7} be a set of complex numbers. Then min_z ∈ S|(z+1/2(5+3 i))| is equal to:2026
- Let S={z ∈ C: 4 z^2+z̄=0}. Then Σ_z ∈ S|z|^2 is equal to:2026
- If α+i β and γ+i δ are the roots of x^2-(3-2 i) x-(2 i-2)=0, i=√-1, then α γ+β δ is equal to:2025
- If α is a root of the equation x^2+x+1=0 and Σ_k=1^n(α^k+1/(α^k))^2=20, then n is equal to ____.2025
- Let S={z=x+i y: (2 z-3 i)/(4 z+2 i). is a real number }. Then which of the following is NOT correct?2023
- Let z be a complex number such that |z+2|=|z-2| and ((z+3)/(z-i))=(π)/4. Then |z|^2 is equal to:2026
- Let the circles C_1:|z|=r and C_2:|z-3-4 i|=5, z ∈ C, be such that C_2 lies within C_1. If z_1 moves on C_1, z_2 moves on C_2 and min |z_1-z_2|=2,…2026
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.