I'm studying numerical analysis and in the book I'm reading there is a theorem thats find a raduis such that all the roots of a polynomial $P$ (with coefficient in $\mathbb{C}$) are in the open disk with center at $(0,0)$. This can be helpful when trying to find roots as it gives a good initial guess.
The only problem I have is that I can't seem to be able to understand why this is true :
$|P(z)| \geq |a_n z^n| - |a_{n-1}z^{n-1}+ \cdots +a_1z+a_0|.$
($P(z)= \sum_{i = 0}^n a_i z^i$)
*also assume $|z| > 1$.