Question

. Express the roots of the equation z3 − α3 = 0 in terms of α and w, where w is a complex cube root of unity. Use your answer to find the roots of the following equations in the form a + ib.

Answer 1

$z_1=\alpha$

$z_2=\alpha w=\alpha(-1/2+i\sqrt{3}/2)$

$z_3=\alpha w^2=\alpha(-1/2-i\sqrt{3}/2)$