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MathImage


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On the figure above a rectangle shape is simplified as a collection of four points. To rotate the rectangular shape, each point is represented as a complex number with a known angle. The set of points forming the rectangular shape is effectively rotated by adding an angle to the original angles.

A sinusodal complex wave animation

Complex Numbers on Wikipedia

Complex Numbers in Trigonometry and Vectors

Complex numbers and similarity constants
Here, complex numbers generate sphinx figures and form a neat spiral known as a loxodrome.