Solve z^3 = 8*i in complex numbers.
$$z^3 = 8i$$
$$ \sqrt[3]{z^3} = \sqrt[3]{8i} \Rightarrow \sqrt[3]{8i} = \sqrt[6]{-64}$$
$$= -2i, i - \sqrt{3}, \sqrt{3} + i$$
$\square$
More generally, we have: