Mathematics · 2024
JEE Main · 29 January 2024, Shift 2 · Q2
Let r and θ respectively be the modulus and amplitude of the complex number z=2-i(2 tan (5 π)/8), then ( r, θ) is equal to
Let r and $\displaystyle \theta$ respectively be the modulus and amplitude of the complex number $\displaystyle z=2-i\left(2 \tan \frac{5 \pi}{8}\right)$, then $\displaystyle (\mathrm{r}, \theta)$ is equal to
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle \left(2 \sec \frac{3 \pi}{8}, \frac{3 \pi}{8}\right)$
More from Complex Numbers
- 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 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
- Let the product of ω_1=(8+i) sin θ+(7+4 i) cos θ and ω_2=(1+8 i) sin θ+(4+7 i) cos θ be α+i β, i=√-1. Let p and q be the maximum and the minimum…2025
- Let z be the complex number satisfying |z-5| ≤ 3 and having maximum positive principal argument. Then 34|(5 z-12)/(5 i z+16)|^2 is equal to:2026
JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.