Alternatively one can define complex differentiability of \(f\) at \(z_0\), by claiming the existence of a function \(\Delta\) which is continuous in \(z_0\), such that
\begin{equation*} f(z)=f(z_0)+(z-z_0)\Delta(z). \end{equation*}Indeed, \(\Delta(z_0)=f'(z_0)\).
Remark
- The above given representation implies that \(f\) is continuous in \(z_0\).