Definition:Complex Disk

Definition

A (complex) disk is a ball in the complex plane.

Let $a \in \C$ be a complex number.

Let $R > 0$ be a real number.

Open disk

The open (complex) disk of center $a$ and radius $R$ is the set:

$\map B {a, R} = \set {z \in \C: \cmod {z - a} < R}$

where $\cmod {\, \cdot \,}$ denotes complex modulus.

Closed disk

The closed (complex) disk of center $a$ and radius $R$ is the set:

$\map {\overline B} {a, R} = \set {z \in \C: \cmod {z - a} \le R}$

where $\cmod {\, \cdot \,}$ denotes complex modulus.

Also see

• Definition:Ball

• Results about complex disks can be found here.