Roots of a Polynomial with Complex Coefficients

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The fundamental theorem of algebra states that a polynomial of degree with complex coefficients has values for which . The are called the roots of , with some of them possibly repeated. Thus the polynomial may be factored into linear terms as , where is some complex number. In the case of real coefficients, the roots are real or come in conjugate pairs.

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This Demonstration considers polynomials of the form , with , , complex. The roots are shown as white dots at the centers of black patches.

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Contributed by: Izidor Hafner (February 2016)
Open content licensed under CC BY-NC-SA


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