QJEEM22Ma0253: JEE Main 2022 Mathematics - Class 11 JEEM22Ma0253 Solution: Let A = { z ∈ C :

Question

Verified Solution • 2025–26 Session moderate

Let $A = {z \in C : | \frac{z + 1}{z - 1} | < 1}$ and $B = {z \in C : \arg (\frac{z - 1}{z + 1}) = \frac{2 π}{3}}$ . Then A $\cap$ B is :

A a portion of a circle centred at (0,−13) that lies in the second and third quadrants only
B a portion of a circle centred at (0,−13) that lies in the second quadrant only
C an empty
D a portion of a circle of radius 23 that lies in the third quadrant only

Accepted Answer

| \frac{z + 1}{z - 1} | < 1 \Rightarrow | z + 1 | < | z - 1 | \Rightarrow Re (z) < 0

and

\arg \left(\frac{z-1}{z+1}\right)=\frac{2 \pi}{3}

is a part of circle as shown.

JEE Main 2022 (Online) 26th June Morning Shift Mathematics - Complex Numbers Question 77 English Explanation

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