Circle of Apollonius in Complex Plane/Examples

Examples of Circle of Apollonius in Complex Plane

Example: $\cmod {\dfrac {z - 3} {z + 3} } = 2$

The equation:

$\cmod {\dfrac {z - 3} {z + 3} } = 2$

describes a circle embedded in the complex plane whose radius is $4$ and whose center is $\paren {-5, 0}$.

Example: $\cmod {\dfrac {z - 3} {z + 3} } < 2$

The inequality:

$\cmod {\dfrac {z - 3} {z + 3} } < 2$

describes the exterior of a circle embedded in the complex plane whose radius is $4$ and whose center is $\paren {-5, 0}$.