Question

value of complex cube roots of unity

Answer 1

we know that w is a root of the equation z3-1=0. Therefore, w satisfies the equation z3-1=0. NOTE: since w3=1, hence, wn=wm, where m is the least non-negative remainder obtained by dividing n by 3. Property V: the sum of the three cube roots of unity is zero i.e., w+1+w2=0.

Answer 2

Lets take an example:
Let the cube root of 1 be x, 3^root1 = x. Hence we have here 3 cube roots of unity. First one is real and the other two are conjugate.