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.