JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Complex Numbers

Set $A$ represents the annular region in the complex plane centered at $(1+i)$ with inner radius 1 and outer radius 2. Set $B$ is the intersection of $A$ with the circle centered at $(1-i)$ with radius 1. The distance between centers $(1+i)$ and $(1-i)$ is $|2i|=2$. Since the circle $|z-(1-i)|=1$ passes through the annular region $A$, their intersection $A\cap B$ forms an arc, which contains infinitely many points. Therefore, $B$ is an infinite set.