MathNet 2019-part-05 — 184 problems (EN–VI) Question 120

Let $n \in \mathbb{N}^*$ and $E(z) = |z+1| + |z^{2n} + 1|$, $z \in \mathbb{C}$. Find
$$ \min\{E(z) \mid z \in \mathbb{C}\}. $$