- #1

jjangub

- 24

- 0

## Homework Statement

Locate and classify the singularities of the following functions

a) f(z) = 1 / (z^3*(z^2+1))

b) f(z) = (1 - e^z)/z

c) f(z) = 1 / (1-e^z(^2))

d) f(z) = z / (e^(1/z))

## Homework Equations

## The Attempt at a Solution

I am not sure what I need to do when it asks me to locate and classify the singularities. I tried this way.

a) f(z) has singularities when z = i or -i and singularities are fifth order poles.

(z^3*(z^2+1) = z^5 + z^3

b) f(z) has essential singularity at 0 because f(z) is defined in the whole complex plane except for z = 0.

c) f(z) has essential singularity at 0 because f(z) is defined in the whole complex plane except for z = 0.

d) since we know e^(1/z) is essential singularity at 0, f(z) = z / (e^(1/z)) is same.

Did I do right?

Please tell me if I did something wrong.

Thank you.