Where is the function differentiable on the complex domain?

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The discussion revolves around determining where a given complex function is analytic in the complex domain. The user applied the Cauchy-Riemann equations and concluded that the function is not analytic anywhere, except potentially at the point (0,0). However, a clarification was made that "complex differentiable" and "analytic" are not equivalent unless the function is differentiable on an open set. The confusion stems from the interpretation of the conditions derived from the equations. Ultimately, the function is only differentiable at (0,0) and not along the line x=y.
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Homework Statement



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

http://img641.imageshack.us/img641/70/97822806.jpg

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

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

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