Complex analytic functions

[asi123]

Homework Statement

Hey guys.
I hope this is the right place to post this question.

http://img641.imageshack.us/img641/70/97822806.jpg [Broken]

I have this "simple" complex function, and I need to decide where this function is analytic in the complex domain.
So, I used the cauchy riemann equations as you can see, and I got to the condition x=y in order for this function to have a derivation. I know that this function is not analytic anywhere on the complex domain.
Now, according to the solution we got, this function has derivation only in (0,0), is this true, shouldn't it be on all x=y?

Sorry for the bad English.
Thanks a lot.

Homework Equations

The Attempt at a Solution

 

[Count Iblis]

You mean "complex differentiable" here, not "analytic" (the equivalence does not hold unless the function is differentiable on some open set).