Set Union/Examples/2 Circles in Complex Plane

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Example of Set Union

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 $A \cup B$ can be illustrated graphically as:


where the union is depicted in yellow.