试证 C．－R．方程的极坐标形式为
$\frac{\partial u}{\partial r}=\frac{1}{r} \frac{\partial v}{\partial \theta}, \frac{\partial v}{\partial r}=-\frac{1}{r} \frac{\partial u}{\partial \theta}$ ，并且 $f^{\prime}(z)=\frac{r}{z}\left(\frac{\partial u}{\partial r}+ i \frac{\partial v}{\partial r}\right)=\frac{1}{z}\left(\frac{\partial v}{\partial \theta}- i \frac{\partial u}{\partial \theta}\right)$ ．