- #1

saraaaahhhhhh

- 22

- 0

## Homework Statement

In the title: f(z) = sqrt(|xy|)...show that this satisfies the Cauchy-Riemann equations at z=0, but is not differentiable there.

## Homework Equations

Cauchy-Riemann just states that partial u partial x = partial v partial y and partial u partial y = - partial v partial x.

## The Attempt at a Solution

I think all the partials du/dx, du/dy, dv/dx, and dv/dy are 0. Because f(0) is 0 in this case, right? Maybe that's wrong. Maybe I'm assumign too much by saying that if z=0, x and y also are 0.

Anyway, then I just need to show the limit as h->0 for differentiation doesn't exist, right? If what I said above is right, than it would just be plugging in some x_0 and y_0 (if h = x_0 + iy_0) for x and y and than finding the limit for when x_0 = 0 and when y_0 = 0, and as long as those aren't equal then it's not differentiable.

Does this sound right, or totally off?