Complex Polynomials

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Four points in the complex plane can be the roots of a complex polynomial of degree four. Solid lines indicate where the real part is zero and dashed lines indicate where the imaginary part is zero. These lines intersect at the chosen roots. The successive derivatives of the complex polynomial behave similarly. Complex points can be added or removed with Alt+Click. Hover over a point to see its value. Notice that derivative roots all lie within the convex hull of the original roots, due to the Lucas–Gauss theorem (linked below).

Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.