is the metric space with metric . Prove:
, for all , where
Not sure what's going on here so I started going backwards for the hell of it:
Is this correct or useful in any way? Can somebody explain this geometrically?
Well that does clear away the clutter.
Any complex number can be written as where .
The points are on the unit circle for any .
The line determined by intersects the unit circle at .
So the real numbers represent the distances of points on the unit circle at minimum and maximum from .