Plotting Rational Functions of a Complex Variable

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This Demonstration shows a complex rational function as a contour plot superposed on a parametric plot, in which colors depend on the quadrant in which
falls. A rational function is the quotient of two polynomials,
and
. This Demonstration uses polynomials of the form
and
, where the coefficients
and
are complex numbers. Suppose that
and
have no common roots. Then the zeros of
are the zeros of
, and the zeros of
are the poles of
. Zeros are shown in white in the centers of the black patches, and poles are shown as black points.
Contributed by: Izidor Hafner (March 2016)
Open content licensed under CC BY-NC-SA
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"Plotting Rational Functions of a Complex Variable"
http://demonstrations.wolfram.com/PlottingRationalFunctionsOfAComplexVariable/
Wolfram Demonstrations Project
Published: March 30 2016