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!

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- Oct 29th 2008, 07:24 PMshadow_2145Number of zeros in each domain (Complex Analysis)
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! - Oct 30th 2008, 03:07 AMOpalg
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. - Oct 30th 2008, 03:15 AMwhipflip15
Very nice.