Set Union/Examples/3 Circles in Complex Plane

Example of Set Union

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

where the union is depicted in yellow.

1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Point Sets: $123 \ \text{(b)}$