 Solution

The modulus obeys $|z{|}^4=4$, giving $|z|=\sqrt{2}$. The complex argument obeys $4\arg z=\pi /2$ modulo $2\pi$. The four distinct complex roots are thereforeThey form a square centred at the origin, on the circle of radius $\sqrt{2}$, with the first vertex at argument $\pi /8$.