Equation of Circle in Complex Plane/Examples/1 less than mod (z + i) not greater than 2

Example of Use of Equation of Circle in Complex Plane

The inequality:

$1 < \cmod {z + i} \le 2$

describes the inside of the annulus whose center is at $-i$, whose inner radius is $1$ and whose outer radius is $2$.

This annulus does not include its inner boundary, but does include its outer boundary.

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Graphical Representation of Complex Numbers. Vectors: $73 \ \text {(a)}$