Solve the following in cartesian form:
$\displaystyle z^4=16$
$\displaystyle \displaystyle z^4 = 16$
$\displaystyle \displaystyle z^4 - 16 = 0$
$\displaystyle \displaystyle (z^2)^2 - 4^2 = 0$
$\displaystyle \displaystyle (z^2 - 4)(z^2 + 4) = 0$
$\displaystyle \displaystyle z^2 - 4 = 0$ or $\displaystyle \displaystyle z^2 + 4 = 0 $
$\displaystyle \displaystyle z^2 = 4$ or $\displaystyle \displaystyle z^2 = -4$
$\displaystyle \displaystyle z = \pm 2$ or $\displaystyle \displaystyle z = \pm 2i$.
So the solutions are $\displaystyle \displaystyle z = -2, z = 2, z = -2i, z = 2i$.