find all solutions of the equation

Question

1. x^3+27=0

2. x^3-8=0

Answer 1

27+0 i = 27 e^i(0) = 27 cos 0 + i sin 0

27^(1/3)=3e^0 or 3e^i(2pi/3) or 3e^(4 pi/3)

= 3
or
= 3 cos 120 + 2i sin 120
= -1.5 + i sqrt 3
or
= -1.5 - i sqrt 3