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 and .
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.
@ arbolis: Look at the attachment at your own discretion. I have the whole thing worked out...but it may be different from what you're supposed to do.