At what points, if any, is $f(z)$ analytic?
$f(z)=(2x+y−x^2y)+i(3+2y−xy^2).$
Please help, very confused..
I know how to compare the C-R equations and know how to find them. One set yields the unit circle. I am supposed to answer at what points is $f(z)$ analytic, how do I state that? Where is it analytic? Or is it nowhere analytic? Thanks..
For a function to be analytic at a point, it needs to satisfy Cauchy-Riemann not only at that point but in an entire open neighborhood of the point. So if you found that Cauchy-Riemann was satisfied only on the unit circle, $f(z)$ would be analytic nowhere, since there is no nonempty open set on which Cauchy-Riemann is satisfied.