This should work with recent desktop versions of Chrome or Firefox and hopefully also on a tablet. It was coded using Vanilla JS.

You are seeing two copies of the complex plane. The left half shows the coefficients $a_0$ to $a_{n-1}$ of a monic polynomial of degree $n$, i.e., the point with the number $k$ in it represents the complex number $a_k$. The right half shows the $n$ roots of this polynomial. You can move (with the mouse or your finger) both the coefficients and the roots around and observe what happens. (You can also fine-tune the position of the last point you moved with the arrow keys. The 0 and 1 keys will set this point exactly to the corresponding value.) Clicking one of the numbers in the middle or typing the corresponding number will switch the degree of the polynomial.

Copyright (c) 2024, Prof. Dr. Edmund Weitz. Impressum, Datenschutzerklärung.