The Complex Unit Circle

The points of the complex unit circle can be parametrized:
,
.
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.
  • Contributed by: Michael Trott with permission of Springer
  • From: The Mathematica GuideBook for Graphics, second edition by Michael Trott (© Springer, 2008).

SNAPSHOTS

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DETAILS


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.

PERMANENT CITATION

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