2008 AMC 12A Question 23 - thichhoctoan.com

Question 23

The solutions of the equation $$
z^4 + 4z^3 i - 6z^2 - 4zi - i = 0
$$ are the vertices of a convex polygon in the complex plane. What is the area of the polygon?

$2^{\frac{5}{8}}$
$2^{\frac{3}{4}}$
$2$
$2^{\frac{5}{4}}$
$2^{\frac{3}{2}}$