Disk

The set of points within a fixed distance of a center: $|z-z_0|<r$ (open) or $|z-z_0|\le r$ (closed).

A disk of radius $r$ centered at $z_0$ is the set of points within distance $r$ of $z_0$ . The open disk $|z-z_0|<r$ excludes its bounding circle; the closed disk $|z-z_0|\le r$ includes it. Complex analysis defaults to open disks almost everywhere, since they are what 'close to $z_0$ , but not equal to it' means for limits and derivatives.

Examples

$|z-i|<2$ is the open disk of radius $2$ centered at $i$ .
$|z|\le 1$ is the closed unit disk.