[tex]x^3-8=0[/tex]
[tex]x^3=8=8\mathrm{cis}\,0^\circ[/tex]
By DeMoivre's theorem, we have
[tex]x=8^{1/3}\mathrm{cis}\left(\dfrac{0^\circ+360^\circ k}3\right)[/tex]
with [tex]k=0,1,2[/tex]. Then we have three solutions,
[tex]x=2\mathrm{cis}\,0^\circ=2[/tex]
[tex]x=2\mathrm{cis}\,120^\circ[/tex]
[tex]x=2\mathrm{cis}\,240^\circ[/tex]
