Finding the number of zeros in the right half plane of $\mathbb{C}$.

Asked May 16 '15 at 23:26

Active May 16 '15 at 23:26

Viewed 302 times

I am attempting to learn an exercise in the chapter on Rouche's Theorem in Ahlfors Complex Analysis. It comes from page 154, number 3:

Find the number of zeros of $$f(z) = z^4 + 8z^3 + 3z^2 + 8z + 3 = 0$$ in the right half plane.

My first thought was to try to use Rouche's Theorem, but this has been to no avail.

Does anyone have any thoughts as to how to approach this problem. I am almost sure that I am going to need to use a semi circle (in the right half plane) centered at zero. The question is how.

asked May 16 '15 at 23:26

Vladhagen

4,878

2

See if roots of $f(z)=z^4+8z^3+3z^2+8z+3=0$ in the right half plane helps. – Alexey Burdin May 16 '15 at 23:58
Ah, yes. Good find. Somehow I was not able to locate that. – Vladhagen May 17 '15 at 00:03

Finding the number of zeros in the right half plane of $\mathbb{C}$.

0 Answers0