由函数解析可得的一个结论

若函数 \(f(z)\) 解析, 设 \(f'(z) = a + ib\), 则

\[a = \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} \]

\[-b = \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x} \]