Question

if W is a complex cube root of unity then find (1+W)(1+W²)(1+W⁴)(1+W⁸)​

Answer 1

Step-by-step explanation:

1, w, w2 are cube roots of unity. 1 + w + w2 = 0, w3 = 1

(1+w)(1+w2)(1+w4)(1+w8)

=(−w2)(w)(1+w3⋅w)(1+(w3)2⋅w2)

=−w3(1+w)(1+w2)

=−1(−w2)(−w)

=w3

=1