Set Intersection/Examples/2 Circles in Complex Plane
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Example of Set Intersection
Let $A$ and $B$ be sets defined by circles embedded in the complex plane as follows:
| \(\ds A\) | \(=\) | \(\ds \set {z \in \C: \cmod {z - 1} < 3}\) | ||||||||||||
| \(\ds B\) | \(=\) | \(\ds \set {z \in \C: \cmod {z - 2 i} < 2}\) |
Then $A \cap B$ can be illustrated graphically as:
where the intersection is depicted in yellow.
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Solved Problems: Miscellaneous Problems: $49 \ \text{(a)}$