Polar form of the Cauchy-Reimann equations is

\frac{\partial u}{\partial r} = r \frac{\partial v}{\partial θ} and \frac{\partial v}{\partial r} = - r \frac{\partial u}{\partial θ}

\frac{\partial u}{\partial r} = \frac{1}{r} \frac{\partial v}{\partial θ} and \frac{\partial v}{\partial r} = - \frac{1}{r} \frac{\partial u}{\partial θ}

Answer

\frac{\partial u}{\partial r} = \frac{1}{r} \frac{\partial v}{\partial θ} and \frac{\partial v}{\partial r} = - r \frac{\partial u}{\partial θ}

\frac{\partial u}{\partial r} = r \frac{\partial v}{\partial θ} and \frac{\partial v}{\partial r} = - \frac{1}{r} \frac{\partial u}{\partial θ}

Answer: Option B

Answer: Option B

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