I'm trying to find roots to a polynom using Rouche's theorem.

Rouche's

I'm feeling unsure of how to calculate the absolute values, if anyone could help...

I'll try an example, taken from wikipedia.

let and

Examine |z| = 1

If I've done this correctly, can I deduce that there's no roots in |z| = 1? If not, how would I show that there's no roots in |z| = 1?

Comments

Please point out errors in my calculation. Furthermore, if I examine |z| = 2 I get |f(z)| - |g(z)| = 31 and |f(z) - g(z)| = 19 which indicates that there are 5 roots inside |z| = 2. Or..?