Question

3) If w is a complex cube root of unity, find the
value of
1
i) w+-
ii) w2+W3+w4 iii) (1+w2)3 -
W
iv) (1-w-w2)3 + (1-w+w2)
30
v) (1+w)(1+w)(1+w^)(1+w)​

Answer 1

Answer:

(ii) w^2+w^3+w^4 = w^2(1+w+w^2) = w^2(0) = 0

(iii) (1+w^2)^3-w = (1+w+w^2-w)^3 - w = (-w)^3 - w = - 1-w