Complex numbers questions from JEE advanced 2020.
Let S be the set of all complex numbers z satisfying |z^2+z+1|=1. Then which of the following statements is/are TRUE?
(A) |z+1/2|≤1/2 for all z ∈ S
(B) |z|≤2 for all z ∈ S
(C) |z+1/2|≥1/2 for all z ∈ S
(D) The set S has exactly four elements
Ans: B, C
For a complex number z, let Re(z) denote the real part of z. Let S be the set of all complex numbers z satisfying z^4−|z|^4=4iz^2, where i=√(−1) . Then the minimum possible value of |z1 −z2|^2, where z1, z2 ∈ S with Re(z1) greater than 0 and Re(z2) less than 0, is _____
Ans: 8
Time stamps:
0:00 Channel intro
0:04 Intro
0:14 First question ( Jee adv 2020 Paper 1, Q9)
0:27 Second question ( Jee adv 2020 Paper 2, Q1)
0:57 Solution to first question
1:14 Option D
5:48 Option A
7:14 Option C
11:02 Option C using geometrical interpretation
13:01 Option B
15:07 Solution to second question
