Question 98
Suppose $a, b \in \mathbb{R}$. If equation
$$(z^2 + az + b)(z^2 + az + 2b) = 0$$
about $z$ has four mutually different complex roots $z_1, z_2, z_3, z_4$ and their corresponding points in the complex plane are exactly four vertices of a square with side length $1$, then find the value of $|z_1| + |z_2| + |z_3| + |z_4|$.
$$(z^2 + az + b)(z^2 + az + 2b) = 0$$
about $z$ has four mutually different complex roots $z_1, z_2, z_3, z_4$ and their corresponding points in the complex plane are exactly four vertices of a square with side length $1$, then find the value of $|z_1| + |z_2| + |z_3| + |z_4|$.