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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, a complex polygon is a polygon in the complex Hilbert plane, which has two complex dimensions. A complex number may be represented in the form (a + ib), where a and b are real numbers, and i is the square root of 1. 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 is really two dimensions, but of different kinds. The unitary plane comprises two such complex planes, which are orthogonal to each other. Thus it has two real dimensions x and y, and two imaginary dimensions ix and iy. A complex polygon is a two-dimensional example of the more general complex polytope in higher dimensions. In a real plane, a visible figure can be constructed as the real conjugate of some complex polygon.