of the complex unit circle
can be parametrized:
This Demonstration shows 3D projections of the surface
space. The angles
denote the rotation angles inside the
hyperplane. In the limit, as
, the complex unit circle becomes a circle in the
For a detailed discussion of the complex unit circle, see
R. Hammack, "A Geometric View of Complex Trigonometric Functions," College Mathematics Journal
(3), 2007 pp. 210-217.
From: The Mathematica GuideBook for Graphics
, second edition by Michael Trott
(© Springer, 2008).