Rational Functions with Complex Coefficients

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A quotient of two polynomials and
,
, is called a rational function. This Demonstration plots rational functions using 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 centers of black patches, and poles are shown as red points.
Contributed by: Izidor Hafner (February 2016)
Open content licensed under CC BY-NC-SA
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"Rational Functions with Complex Coefficients"
http://demonstrations.wolfram.com/RationalFunctionsWithComplexCoefficients/
Wolfram Demonstrations Project
Published: February 22 2016