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.