Find the number of zeros in each of the domains.
(1)
(a)
(b)
(c)
(d)
I have no idea how to approach these. If someone could help me out or point me in the right direction for one of these, I would appreciate it. Thanks!
Find the number of zeros in each of the domains.
(1)
(a)
(b)
(c)
(d)
I have no idea how to approach these. If someone could help me out or point me in the right direction for one of these, I would appreciate it. Thanks!
Use Rouché's theorem. In each case, find the dominant term (or terms) for that value of |z|, and apply the theorem.
To take part (b) as an example, when |z|=1 it's clear that . By Rouché's theorem, has the same number of zeros inside the circle |z|=1 as , namely 7.