Polar form of the Cauchy-Reimann equations is
A. $$\frac{{\partial {\text{u}}}}{{\partial {\text{r}}}} = {\text{r}}\frac{{\partial {\text{v}}}}{{\partial \theta }}{\text{ and }}\frac{{\partial {\text{v}}}}{{\partial {\text{r}}}} = - {\text{r}}\frac{{\partial {\text{u}}}}{{\partial \theta }}$$
B. $$\frac{{\partial {\text{u}}}}{{\partial {\text{r}}}} = \frac{1}{{\text{r}}}\frac{{\partial {\text{v}}}}{{\partial \theta }}{\text{ and }}\frac{{\partial {\text{v}}}}{{\partial {\text{r}}}} = - \frac{1}{{\text{r}}}\frac{{\partial {\text{u}}}}{{\partial \theta }}$$
C. $$\frac{{\partial {\text{u}}}}{{\partial {\text{r}}}} = \frac{1}{{\text{r}}}\frac{{\partial {\text{v}}}}{{\partial \theta }}{\text{ and }}\frac{{\partial {\text{v}}}}{{\partial {\text{r}}}} = - {\text{r}}\frac{{\partial {\text{u}}}}{{\partial \theta }}$$
D. $$\frac{{\partial {\text{u}}}}{{\partial {\text{r}}}} = {\text{r}}\frac{{\partial {\text{v}}}}{{\partial \theta }}{\text{ and }}\frac{{\partial {\text{v}}}}{{\partial {\text{r}}}} = - \frac{1}{{\text{r}}}\frac{{\partial {\text{u}}}}{{\partial \theta }}$$
Answer: Option B
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