Set Intersection/Examples/3 Circles in Complex Plane
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Example of Set Intersection
Let $A$, $B$ and $C$ be sets defined by circles embedded in the complex plane as follows:
\(\ds A\) | \(=\) | \(\ds \set {z \in \C: \cmod {z + i} < 3}\) | ||||||||||||
\(\ds B\) | \(=\) | \(\ds \set {z \in \C: \cmod z < 5}\) | ||||||||||||
\(\ds C\) | \(=\) | \(\ds \set {z \in \C: \cmod {z + 1} < 4}\) |
Then $A \cap B \cap C$ 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: Supplementary Problems: Point Sets: $123 \ \text{(a)}$