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If w is a non real cube root of unity then the expression (1-w)(1-w^2)(1+w^4)(1+w^8) is equal to

If w is a non real cube root of unity then the expression (1-w)(1-w^2)(1+w^4)(1+w^8) is equal to

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1 Answers

Arun
25750 Points
6 years ago
Dear student
 
Use 1 + w +w² = 0
&
w³ = 1
 
Now
 
(1-w)(1-w²)(1+w⁴)(1+w^8)
= (1-w) (1-w²)(1+w)(1+w²)
= (1-w²)(1-w⁴)
= (1-w²)(1-w)
= (1-w-w²+w³l
= (1 -(w+w²) +1)
= (1 -(-1) +1)
= (1+1+1)
= 3
 
 
Regards
Arun (askIITians forum expert)

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