Complex polygon

[1] A complex number may be represented in the form

A complex number lies in a complex plane having one real and one imaginary dimension, which may be represented as an Argand diagram.

So a single complex dimension comprises two spatial dimensions, but of different kinds - one real and the other imaginary.

A complex polygon is a (complex) two-dimensional (i.e. four spatial dimensions) analogue of a real polygon.

In a real plane, a visible figure can be constructed as the real conjugate of some complex polygon.

A formula relating an integral over a bounded region to a closed line integral may still apply when the "inside-out" parts of the region are counted negatively.

Moving around the polygon, the total amount one "turns" at the vertices can be any integer times 360°, e.g. 720° for a pentagram and 0° for an angular "eight".