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

Let

and

be the polar coordinates in the plane (complex I guess?), let

be a function of the complex plane in itself. (I guess they mean

.)

Using the fact that

in which

and

are real differentiable functions of

and

, show that the Cauchy-Riemann equations in polar coordinates are written as

.

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.