Mathematics · 2014
JEE Main · 12 April 2014, Shift 1 · Q62
Let z ≠-i be any complex number such that (z-i)/(z+i) is a purely imaginary number. Then z+1/z is:
Let $\displaystyle z \neq-i$ be any complex number such that $\displaystyle \frac{z-i}{z+i}$ is a purely imaginary number. Then $\displaystyle z+\frac{1}{z}$ is :
Official answer
(3)
any non-zero real number.
More from Complex Numbers
- The point represented by 2+i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there 2 √2 units in the…2016
- 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 z=((√3)/2+i/2)^5+((√3)/2-i/2)^5. If R(z) and I(z) respectively denote the real and imaginary parts of z, then:2019
- 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
JEE Main 2014 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.