Problem 1526 (difficulty: 8/10)

Let \(\displaystyle f\in \C[x]\) and let \(\displaystyle T\) be a rectangle such that \(\displaystyle f\) has no root on the boundary of \(\displaystyle T\). Show that the number of roots of \(\displaystyle f\) inside \(\displaystyle T\) agrees with the winding number about \(\displaystyle 0\) of the image of the boundary of \(\displaystyle T\) under \(\displaystyle f\).

Give me another random problem!