Suppose we have a system of complex polynomials $f = (f_1, \ldots, f_n)$, where each $f_i$ can be viewed as a function $\mathbb{C}^n \to \mathbb{C}$. The *solutions* of $f$ are the points $x \in \mathbb{C}^n$ such that $f(x) = 0$.

There are results bounding the magnitude of the zeros of univariate polynomials. One result for instance is given here. With this result we know that all zeros of a univariate polynomial $p$ are inside a complex disk or radius $R$ centered at the origin. The value $R$ can be determined using only the coefficients of $p$.

In the title, by *simple set* I mean a set like the above, which is a disk. What I mean by simple is a set which is determined explicitly by the coefficients of the $f_i$'s and has some simple determining rule. I'm looking for a way to know where the solutions are in advance. Sharp results are welcome.

I know there are some results relating this systems with Newton polyhedra, but I only saw results about counting solutions. If there is a connection between Newton polyhedra and the location of the solutions I would be glad to know. If anyone know some relevant article or book please share it here so I can read it.

Thank you very much.