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The Complex Unit Circle

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The points of the complex unit circle can be parametrized:

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,

.

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.

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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

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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.

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