Consider a polynomial $$p(z) = z^6 + 9z^4 + z^3 + 2z + 4 $$
I need to find which quadrant of the complex plane contains how many zeros that lie in unit circle. Also, I need to find which quadrant contains the two zeros of $p(z)$ that lie outside the unit circle.
By using Rouche's theorem, I have found that there are four zeros of $p(z)$ that lie inside the unit circle. But I am not sure how to assign them quadrants. Likewise for the zeros that are outside the unit circle.