Solution

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This is an example of a chaotic system. Try increasing the limits of t. You will see that the curve slowly fills the entire unit square.

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A complex number can be represented as z=x+yi,and graphically in the complex plane,where the real part of z is its x-coordinate and the imaginary part is the y-coordinate.Furthermore, the exponent function for a complex argument is =cos x+i sin x, so the above parametric graph represents the unit circle in xy-plane.

Created by Mathematica  (April 10, 2007)