Solution
= Solution
The <modulus> obeys $|z|^4=4$, giving $|z|=\sqrt2$. The <complex argument> obeys $4\arg z=\pi/2$ modulo $2\pi$. The four distinct <complex roots> are therefore
$$
\boxed{z_k=\sqrt2\exp\left[i\left(\frac\pi8+\frac{k\pi}2\right)\right],\qquad k=0,1,2,3.}
$$
They form a square centred at the origin, on the circle of radius $\sqrt2$, with the first vertex at argument $\pi/8$.