Where is the function differentiable on the complex domain?

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SUMMARY

The discussion centers on determining the differentiability of a complex function using the Cauchy-Riemann equations. The user concludes that the function is not analytic anywhere in the complex domain, except at the point (0,0). This conclusion is confirmed by the clarification that "complex differentiable" and "analytic" are not equivalent unless the function is differentiable on an open set. The key takeaway is that the function's differentiability is restricted to the single point (0,0).

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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.


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The Attempt at a Solution

 
Last edited by a moderator:
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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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