Allen

Find the maximum value M of |f(z)| on |z|=1

for f(z) = z^2/(2z-3) and z is a complex variable

classify the isolated singularities of

f(z) = log(z)/(z^2-3z+2)

I factored the denominator as (z-1)(z-2)

and said that 1 and 2 are both simple poles...

am I on the right track??

∫ (e^z - 1)/(1 - cos(z)) where the contour is the

circle |z|=π

I tried using cauchy formula for derivatives but i'm

not sure if that is the way to go....i ended up with

1/(2πi) as the answer???

∫(e^z + z + 1) / z^2 where the contour is the circle

|z|=1 oriented positively

∫(e^z+z+1)/(z^2) where the contour is the circle

|z|=1 oriented positively

Classify isolated singularities and find corresponding residue

of f(z)=(1-z^n) / (1-z^2) where n is in the set of natural numbers

Any hints would be awesome...im very stuck on this...

need to find the first 3 nonzero terms of the Laurent expansion

of f(z) = e^(2z+2) / (z+1) where z is not equal to -1.

I tried to rewrite it and somehow use a taylor

expansion but I can't get it to work...super confused!

find the laurent series for f(z)=cos(πz) / (z-π)

centered at π and valid for z not equal to π

find the radius of convergence and the (open) disk of convergence of the power series

SUM [(-1)^n(z+i)^n] / (1-i)^n from 0 to infinity

∫( ln(z+2)/z^2 ) dz

over gamma; where gamma is the positively oriented

circle of radius 1 centered at 0

let f be an entire function that has the property that

|e^(f(z))| ≥ 1 for all z in C. Show that f is constant.

let f be analytic in the disk |z+1| ≤ 4 and suppose that |f(z)| ≤ 1

for all z such that |z+1| ≤ 4.

Use Cauchy's inequalities to find an upper bound on |f''(-1)|.