Thread: CR equations and analyticity??

I have a serious doubt. In general given a function f(z)=x^2 + i y^2.
When it is asked to determine the analyticity of the function, is it sufficient to check only for the CR equations?? Please note that there is no specific point or neighbourhood mentioned? Now what is the right approach ? Please anyone kindly help me..........

Originally Posted by rsashwinkumar

I have a serious doubt. In general given a function f(z)=x^2 + i y^2.
When it is asked to determine the analyticity of the function, is it sufficient to check only for the CR equations?? Please note that there is no specific point or neighbourhood mentioned? Now what is the right approach ? Please anyone kindly help me..........

Yes, it is sufficient if the partial derivatives are continuous. At any rate, the equations are necessary.

Tonio