- #1

saraaaahhhhhh

- 22

- 0

## Homework Statement

The functions Re(z)/|z|, z/|z|, Re(z^2)/|z|^2, and zRe(z)/|z| are all defined for z!=0 (z is not equal to 0)

Which of them can be defined at the point z=0 in such a way that the extended functions are continuous at z=0?

It gives the answer to be:

Only f(z)=zRe(z)/|z|, f(0)=0

I see that f(0)=0 in this case, but I don't see how this is proven or shown. I don't see why the last equation works and the first three don't.

## The Attempt at a Solution

I'm completely unsure of how to do this, I would have something if I even knew where to start. Maybe I'm confused about what extended functions are?

A link to the book:

http://books.google.com/books?id=Oy...ver&dq=introductory+complex+analysis#PPA37,M1