The Complex Unit Circle
The points of the complex unit circle can be parametrized:[more]
This Demonstration shows 3D projections of the surface in space. The angles denote the rotation angles inside the hyperplane. In the limit, as , the complex unit circle becomes a circle in the plane.[less]
Contributed by: Michael Trott with permission of Springer (March 2011)
From: The Mathematica GuideBook for Graphics, second edition by Michael Trott (© Springer, 2008).
Open content licensed under CC BY-NC-SA
For a detailed discussion of the complex unit circle, see
R. Hammack, "A Geometric View of Complex Trigonometric Functions," College Mathematics Journal, 38(3), 2007 pp. 210-217.