Mathematics · 2021
JEE Main · 22 July 2021, Shift 2 · Q78
Let n denote the number of solutions of the equation z^2+3 z̄=0, where z is a complex number. Then the value of Σ_k =0^∞ 1/(n^k) is equal to:
Let n denote the number of solutions of the equation $\displaystyle z^2+3 \bar{z}=0$, where $\displaystyle z$ is a complex number. Then the value of $\displaystyle \sum_{\mathrm{k}=0}^{\infty} \frac{1}{\mathrm{n}^{\mathrm{k}}}$ is equal to:
Official answer
(4)
$\displaystyle \frac{4}{3}$
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
- If Re((z-1)/(2 z+i))=1, where z=x+i y, then the point (x, y) lies on a:2020
- 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 z=(√3-i)/2 and (z^95+i^95)^94=z^n, then the minimum positive integral value of ' n ' is \ \ \ \.2021
- If z=2+3 i, then z^5+(z̄)^5 is equal to:2022
- 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
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.