Wolfram Demonstrations Project

The points

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

plane.

Contributed by: Michael Trott with permission of Springer
From: The Mathematica GuideBook for Graphics, second edition by Michael Trott (© Springer, 2008).

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.

Contributed by: Michael Trott with permission of Springer

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The Complex Unit Circle