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Complex Analysis. How does this equation satisfy the Cauchy Riemann equation at the origin. When I take the partial derivative of u = sqrt(xy) in terms of x, I get y/2(sqrt(xy)) which is undefined at the z = 0? Then how does it satisfy the Cauchy Riemann equation. Is my partial derivative of u in terms of x wrong?


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Screen Shot 2020-07-13 at 9.44.32 PM.png
Exercise II.6.2. Prove that the function f (z) = vry is not differentiable
at the origin, even though it satisfies the Cauchy-Riemann equations there.

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