Recent content by brianhawaiian

double pole at i/2 and -i/2? Edit: Actually simple pole at z = 0?

Homework Statement integral |z|=1 of sinz/z2dz Homework Equations Rule #1 if f(z) has a simple pole at z0, then Res[f(z),z0] = lim(as z goes to z0) (z - z0)*f(z) Rule #2 if f(z) has a double pole at z0, then Res[f(z),z0] = lim(as z goes to z0)d/dz (z - z0)2*f(z) Rule #3 If...

Got it, thanks a million

haha, okay, couldn't I just do 1/(z+1)(z2 + 2z + 2) then 1/(z+1)(z2 + 2z + 2) = A/(z2 + 2z + 2) + B/(z+1) Then 1 = A(z+1) + B(z2 + 2z + 2) First let z = -1 solve for B, so I found B to be 1. Knowing that couldn't I let z = anything, and solve for A?

Homework Statement Sorry I don't have equation editor working 1/(z+1)(z2 + 2z + 2) Homework Equations The Attempt at a Solution (z2 + 2z + 2) z2 + 1) can be factor as (z - i)(z + i) However, I'm having trouble seeing the pattern on what (z2 + 2z + 2) would become, I...

Yeah, I figured it out thanks to you guys, much appreciated, I have another question up on the page, was wondering if you could maybe help with that one? If not it's okay, Thanks again!

Anything?

Homework Statement Find all possible Laurent expansions centered at 0 for (z - 1) / (z + 1) Find the Laurent Expansion centerd at z = -1 that converages at z = 1/2 and determine the largest opens et on which (z - 1) / (z + 1) converges Homework Equations The Attempt at a...

Thank you, appreciate the comments... I'm completely lost in Complex Analysis (First Grad Level class, never took it as an undergrad)

Sorry I don't have equation editor, for some reason every time I install it on Microsoft Word it never appears... Homework Statement Calculate the residue at each isolated singularity in the complex plane e^(1/z) Homework Equations #1 Simple pole at z0 then, Res[f(z), z0] = lim...

Homework Statement "Find the radius of convergence of the power series for the following functions, expanded about the indicated point. 1 / (z - 1), about z = i. Homework Equations 1 / (1 - z) = 1 + z + z^2 + z^3 + z^4 + ... + Ratio Test: limsup sqrt([SIZE="3"]an)^k)^1/k...