Circle-full of roots

Let $P(z) = z^n+z+1, n \geq 2$ . Show that all roots of $P(z)$ lie in the region $|z| \leq \displaystyle\frac{n}{n+e^{a}}$ , where $a\in\mathbb C$ . Find the value of $a$ and enter the answer as $\mathcal{Re}(a)+\mathcal{Im}(a)$