A problem in limit of a complex function

[cng99]

Homework Statement

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?

 

[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.

 

[cng99]

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.

But the answer is zero.

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.

 

[NewtonianAlch]

But the answer is zero.

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.

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.

 

[cng99]

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.

Thanks a lot.