AMC 12 2008a Problem 23

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

$\mathrm{(A)}\ 2^{\frac{5}{8}} \mathrm{(B)}\ 2^{\frac{3}{4}} \mathrm{(C)}\ 2 \mathrm{(D)}\ 2^{\frac{5}{4}} \mathrm{(E)}\ 2^{\frac{3}{2}}$