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## Main Question or Discussion Point

I'm doing a little self study on complex analysis, and am having some trouble with a concept.

From Wikipedia:

"In mathematics, the Cauchy–Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations that provides a necessary and sufficient condition for a differentiable function to be holomorphic in an open set."

But I have a function here, (z*)^2/z, which appears to satisfy the Cauchy-Riemann equations at z = 0, but the function is not differentiable there. Isn't this a contradiction that the above condition is both necessary and sufficient?

From Wikipedia:

"In mathematics, the Cauchy–Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations that provides a necessary and sufficient condition for a differentiable function to be holomorphic in an open set."

But I have a function here, (z*)^2/z, which appears to satisfy the Cauchy-Riemann equations at z = 0, but the function is not differentiable there. Isn't this a contradiction that the above condition is both necessary and sufficient?