Hey guys.

I'm trying to solve an exercise, and the solution is proberbly simpler than what I'm trying to do.

We are given

F = (x^2 + y^2)^{-1} \binom{-y}{x}

The curve C is given by the parametrization

\mathbf{r}(t) = (r(t)\cos(\theta (t)) , r(t) \sin (\theta (t)))

where r and \theta both have continous differentials and r(t) > 0

Then I have shown that
F(\mathbf{r}(t)) \cdot \mathbf{r}'(t) = \theta'(t) and \int _C F \cdot d\mathbf{r} = \theta(b)-\theta(a).

For the part of the excercise I'm having issues with, we are given

f(x,y) = 2 \mbox{Arctan} \frac{y}{x + \sqrt{x^2 + y^2}}.

Now I need to find the domain of f, and show that f is the potential function of F.

I understand that the domain is \{(x,y) | x + \sqrt{x^2+y^2} > 0\}, but can I write it in a prettier way?

I'm getting a hint, that I should convert to polar coordinates as soon as possible, because the calculations will be easier. But I cant really figure out how to solve the excercise. Anyone have some hints? Especially on how, when and why I'm supposed to convert to polar coordinates.

Thanks a million.