Question

prove that

(1-w)(1-w^2)(1-w^4)(1-w^5)=9


w=omega ​

Answer 1

Explanation:

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

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