Liouville height inequality
= Liouville height inequality
{c}
If $\gamma\ne0$ is algebraic of degree at most $D$, then every embedding satisfies
$$
|\gamma|\geq H(\gamma)^{-D}.
$$
Indeed, $H(\gamma^{-1})=H(\gamma)$ and the contribution of one Archimedean place to the height bounds $|\gamma|^{-1/D}$.