Originally Posted by

**arbolis** I'm totally stuck on this exercise. I'd like a hint rather than a full answer.

Let $\displaystyle r$ and $\displaystyle \theta$ be the polar coordinates in the plane (complex I guess?), let $\displaystyle f(z)$ be a function of the complex plane in itself. (I guess they mean $\displaystyle f:\mathbb{C} \to \mathbb{C}$.)

Using the fact that $\displaystyle f(re^{i\theta})=R(r,\theta)e^{i\Theta (r, \theta)}$ in which $\displaystyle R(r,\theta)$ and $\displaystyle \Theta (r,\theta)$ are real differentiable functions of $\displaystyle r$ and $\displaystyle \theta$, show that the Cauchy-Riemann equations in polar coordinates are written as $\displaystyle \frac{\partial R}{\partial r}=\frac{\partial R}{r \partial \theta}=-R \frac{\partial \Theta}{\partial r}$.

I must also show another equation, but I'll ask help if I get stuck.

I don't know how to start the problem. I know the Cauchy Riemann equations, but I don't think I should start by writing them down.