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\paragraph{Example 2.}  Suppose $f: \complex^n \to \reals$ is a real-valued function defined for $x \in \complex^n$. The derivative $Df(x)$ is defined as \\  \begin{align*}  Df(x) = \left[ \frac{\partial f}{\partial x_i}(x) \dots x_i}(x), \dots,  \frac{\partial f}{\partial x_n}(x) \right] \end{align*}