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The Real and Imaginary Zero Sets of a Complex Polynomial

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The four locators are the simple roots of a polynomial of degree four in the complex plane. The solid blue curves plot where the real part of is zero and the dashed blue curves plot where its imaginary part is zero. These lines intersect at the chosen roots.

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The derivative is similar, with solid and dashed green curves. The roots of the derivative lie within the convex hull of the original roots, in accordance with the Lucas–Gauss theorem (linked below).

You can drag the locators, and you add or remove complex roots with Alt+Click. Hover over a point to see its value.

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Contributed by: Ed Pegg Jr (May 8)
Open content licensed under CC BY-NC-SA

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