i'm struggling with the following problem:

Let $f:\mathbb{C}\setminus\{0\}\to\mathbb{R}\_+$, $(x,y)\mapsto\sqrt{x^2+y^2}$. Show that $f$ is open for saturated sets $A$ under the assumption, that $\mathbb{C}\setminus\{0\}$ and $\mathbb{R}\_+$ are equipped with the subspace topology of the euclidean topology.

i know a set $A$ is saturated iff $A=f^{-1}(f(A))$, but i dont know where this comes to use. 

**my attempt:**

i want to show that for $z\in A\subseteq\mathbb{C}\setminus\{0\}$ the set $f(A)$ is a neighborhood of $f(z)$, but how do i compute $f(A)$? since the euclidean topology is just intervals $(x,y)$ i guess i could write $A$ as the product of such intervals, but then i'm stuck.