# Homework Help: A problem in limit of a complex function

1. Apr 12, 2012

### cng99

1. The problem statement, all variables and given/known data
I'm a newbie at complex analysis.

Find:
lim $\frac{\bar{z}^{2}}{z}$
z→0

2. The attempt at a solution
L'Hospital rule gives the answer in no time. But how do you solve without it?

2. Apr 12, 2012

### NewtonianAlch

Well, I think it would help if you read up on how to do limits in complex analysis first.

You basically have to find out the limit as x->0 and y->0. You have to do it twice.

For e.g. as x->0 and then y->0 (1) -- then y->0 and then x->0 (2), this way you might find there are two different limits; this means the limit does not exist.

3. Apr 12, 2012

### cng99

Also can you suggest me some good self-study material to learn complex calculus? I'm good at real number calculus, and I started reading this book called 'Complex Variables Demystified' by David McMohan. But it's the only one I have.

4. Apr 12, 2012

### NewtonianAlch

Yes, well when you calculate this limit you will find out it is zero. It matches.

I'm sure some more experienced users can suggest much better material. I too am fairly new to this stuff. There are plenty of online notes, books, etc though.

5. Apr 12, 2012

### cng99

Thanks a lot.