real axis

“There will be a little bit of moisture from that, and the real axis is split between the Northwest, Southern California and parts of Baja California.”

������ if the set doesn’t come in one convenient piece like the interval between 0 and 1 and it’s a collection of points scattered randomly about the real axis?

Complex here doesn’t mean complicated but refers to the complex plane, a two-dimensional plane with a real axis and an imaginary axis, where complex numbers like 2+3i live.

It can now be easily proved that as z describes the real axis in its plane the point ζ describes once a circle of radius unity, with centre at ζ = 0, and that there is a definite correspondence of point to point between points in the z-plane which are above the real axis and points of the ζ-plane which are interior to this circle; in particular z = i corresponds to ζ = 0.

Herein the points a, b, ... of the real axis give rise to the corners of the polygon; the condition Σα = n − 2 ensures merely that the point t = ∞ does not correspond to a corner; if this condition be not regarded, an additional corner and side is introduced in the polygon.