Understanding "asymptotic" behaviour of a set

Question

In a book, an author defines a complex polynomial \begin{align*} p(z)=\alpha_{n}z^{n}+\alpha_{n-1}z^{n-1}+\cdots+\alpha_{1}z+\alpha_{0},\quad \alpha_{n}\neq0, \end{align*} $n\in\mathbb{N}$ such that $\text{Re }p(z)\geq0$ for $z\in\mathbb{R}$. Further, he claims the set $A=\{z\in\mathbb{C}:\text{Re }p(z)<0\}$ "approaches" the following $n$ sectors \begin{align*} \arg\alpha_{n}+n\arg z \in \left(\frac{\pi}{2},\frac{3\pi}{2}\right)+2m\pi,\quad m=0,\ldots,n-1, \end{align*} for large $|z|$. He says something like $p(z)\approx\alpha_{n}z^{n}$ for large $|z|$, however, what does $\approx$ really mean here? Is there some more explicit way of showing this fact?