# Perturbing the Constant Coefficient of a Complex Polynomial

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This Demonstration plots the complex polynomial . For , the multiplicity of a root determines the number of cycles (cyan, blue, yellow, red) around the root (shown as a black dot). An example is shown in the first snapshot. You can vary , , , , , and . Small changes in the constant term, which makes , transforms the polynomial to a form , with all of the roots of the new polynomial being simple.

Contributed by: Izidor Hafner (June 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

detailSectionParagraph## Permanent Citation

"Perturbing the Constant Coefficient of a Complex Polynomial"

http://demonstrations.wolfram.com/PerturbingTheConstantCoefficientOfAComplexPolynomial/

Wolfram Demonstrations Project

Published: June 19 2017