Complex Numbers
Locus & Sets
MMTS_Full_Test_12
Grade 12
Question:
Let $A=\{z\in\mathbb{C}:1\le|z-(1+i)|\le 2\}$ and $B=\{z\in A:|z-(1-i)|=1\}$. Then $B$:
is an empty set
contains exactly two elements
contains exactly three elements
is an infinite set
Step-by-Step Solution
Key Concept: B is the intersection of an annular region with a circle
The circle $|z-(1-i)|=1$ lies entirely within the annulus $1\le|z-(1+i)|\le 2$, so $B$ is an infinite set.
Correct Answer: 4