Recent content by AcC

Homework Statement Find the number of zeros of the folowing polynomial lying inside the unit circle, f(z)= z^9 - 2z^6 + z^2 - 8z - 2 The Attempt at a Solution Rouche's Theorem says if f and g differentiable which contains a simple loop s and all points inside s...

Take limit e^z as z→-infinity it equal to zero, so it not satisfy the statement. I proved this statement with using Liouville Theorem.

Thanks a lot for hint..:) I have solved this as below; since f is analytic on C so f is differentiable on C, if we use Cauchy's Estimate then we find |f^{(k)}(z)|<=M.|z|^n.k!/|z|^k for k>=n if take lim as z→0 then we find...

Homework Statement Let f be analytic throught C, suppose that |f(z)|<=M|z|^n for a real constant M and positive integer n. Show that f is a polynomial function of degree less than n.

Yes you are true!?? but I found this question in complex analysis book, I tried to solve but I hadnt thought that it could be false..!

Homework Statement Let f:C\rightarrowC be differentiable, with f(z)\neq0 for all z in C. Suppose limf(z) is exist and nonzero as z tends to z0. Prove that f is constant.

Thanks grey_earl but I want to show if A is connected set and A ⊂ B ⊂ cl(A) then B is connected.. I have to show that ""Suppose B=G∪H is a disconnection of B, then using the fact that B ⊂ cl(A) prove that contradict the given A is connected"" How can I show this?

Homework Statement Let A be connected subset of X and let A ⊂ B ⊂ cl(A). Show that B is connected and hence, in particuar, cl(A) is connected. Hint: (Use) Let G∪H be a disconnection of A and let B be a connected subset of A then we see that either B∩H=∅ or B∩G=∅, and so either B⊂G or B⊂H...