Editing Complex polygon (section)

==Geometry==
{{See|Complex polytope#Regular complex polygons}}
In [[geometry]], a complex polygon is a polygon in the complex [[Hilbert space|Hilbert]] plane, which has two [[complex number|complex]] dimensions.<ref>Coxeter, 1974.</ref>

A [[complex number]] may be represented in the form <math>(a + ib)</math>, where <math>a</math> and <math>b</math> are [[real number]]s, and <math>i</math> is the square root of <math>-1</math>. Multiples of <math>i</math> such as <math>ib</math> are called ''[[imaginary number]]s''. 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.

The [[unitary space|unitary]] plane comprises two such complex planes, which are [[orthogonal]] to each other. Thus it has two real dimensions and two imaginary dimensions.

A '''complex polygon''' is a (complex) two-dimensional (i.e. four spatial dimensions) analogue of a real polygon. As such it is an example of the more general [[complex polytope]] in any number of complex dimensions.

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