The original poster presents a limit problem involving a complex function, specifically the limit of \(\frac{\bar{z}^{2}}{z}\) as \(z\) approaches 0. The context is within the subject area of complex analysis.
Some participants express differing views on the limit's existence, with one asserting that the limit is zero while others suggest that multiple approaches may yield different results. There is a request for self-study materials, indicating a desire for further understanding of complex calculus.
Participants mention the need to consider limits as both \(x\) and \(y\) approach zero, highlighting the complexity of limits in the context of complex functions. There is an acknowledgment of varying levels of experience among participants.
NewtonianAlch said: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 said: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 said: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.