Recent content by MurraySt

I'm asked to use Rouche's Theorem to prove Liouville's - I really don't have much of a clue as proofs are not my strong suit. Next up: Find the max and min of abs(f(z)) over the unit disk where f(z) = z^2 - 2 Do I use the maximum modulus theorem?Lastly I'm given epsilon>0 and the set e^(1/z)...

So sorry to bother you one final question: The denominator of my problem is z^2 +4iz -1. I used the quadratic equation to get the answers i(-2+rad3) and i(-2-rad3). Does my denominator simply become the product of the roots? It scares me that I don't get back any z. Thanks as always for your...

As a quick follow-up: If my curve is oriented negatively (clockwise) how does this affect my final answer? Do I simple negate it?

What is the difference between piecewise, uniform and absolute convergence? When I go about proving whether something converges uniformly vs. just converges do I go about the problem differently? If someone could provide rigorous and layman's terms definitions for these that would be great!

I'm integrating 1/(z-1/2) over the closed disk w/ radius = 3 centered at 0. I've seen other problems where the final answer was i2pi times f(w) - here w =1/2. Since f(z) is equal to 1. Is the final answer just i2pi? Next up: I have the integral of dt/(2 + sint) the problem then tells me...

Hope someone could give me some help with a couple of problems. First: Proof of - A function f:G -->Complex Plane is continuous on G iff for every sequence C(going from 1 to infinity) of complex numbers in G that has a limit in G we have limit as n --> infinity f(C) = f(limit as n...

Thanks for the fast reply. By singularity you mean not defined at 0? Such as 1/z?

Thanks in advance for your time and all the wonderful previous answers I've received lurking on this site - its been great! Anyway I have two functions G:[0,2pi] --> Complex Plane and H:[0,4pi] --> Complex Plane Both functions are equal to...