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“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.”

What 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.

The axis Ox is often called the real axis, and the axis Oy the imaginary axis.

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.