Suppose $U \subset \C$ is a domain and $f \colon U \to \C$. Prove that if the following limit exists \begin{equation*} g(z) = \lim_{h \to 0} \frac{f(z+h)-f(z)}{\bar{h}} \end{equation*} for all $z \in U$ (note the bar on the $h$), then $f$ is real differentiable, and satisfies