Question

find a trigonometric representation of the solutions in C (complex numbers) of the equation x^3 -1 = 0

Answer 1

x=1

Answer 2

x^3=1
x^3=cos0+isin0
x=(cos (2k pi +0)+ isin(2k pi+0))^(1/3)
= cos((2k pi)/3) + i sin ((2k pi)/3) (DeMoivre's thm) where k=0,1,2.....