Question

(1-w)(1-w2)(1+w4)(1+w8)=?​

Answer 1

Answer:

We have 1 + w + w2 = 0 & w3 = 1

(1 – w)(1 – w2)(1 – w4)(1 – w5) = (1 – w)(1 – w2)(1 – w3.w)(1 – w3.w2)

= (1 – w)(1 – w2)(1 – w)(1 – w2) (Since w3 = 1)

= (1 – w)2(1 – w2)2

=(1 – 2w + w2)(1 – 2w2 + w4) = (1 – 2w + w2) (1 – 2w2 – w3.w) = (1 – 2w + w2) (1 – 2w2 – w)

= ( – w – 2w)( – w2 – 2w2) (since 1 + w + w2 = 0)

= ( – 3w) ( – 3w2) = 9w3 = 9