analysis - $lim_{t rightarrow infty}frac{t^n z^n}{|t^nz^n + cdots+tz +c|} $?

How to find the limit

$$\lim_{t \rightarrow \infty}\frac{t^n z^n}{|t^nz^n + \cdots+tz +c|} $$
where $c \in\Bbb C$?

is the answer $z^n$? please help :)

Answer

$$\lim_{t\to\infty}\frac{t^n z^n}{|t^nz^n + \ldots+tz +c|}=\lim_{t\to\infty}\frac{z^n}{\left|z^n+\frac{z^{n-1}}{t^{n-1}}+\ldots+\frac{c}{t^n}\right|}=\ldots $$