A brief introduction to complex analysis

\(\underline{Def:}\)A func \(U(\subset \mathbb{C}) \stackrel{f}\longrightarrow \mathbb{C}\)is (complex) differentiable at a point \(z_0 \in intU\)(int:内部)
If f is cpx diff at \(z_0\),we call the limit the (cpx) derivative of f at \(z_0\) and devote it by \(f^{\prime}(z_0)\)or \(\frac{df(z_0)}{dz}\)
if \(U \stackrel{f}\longrightarrow \mathbb{C}\)is (cpx)diff at every z