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if omega(w) is the cube root of unity then(1-w-w^2)^4 is?

if omega(w) is the cube root of unity then(1-w-w^2)^4 is?
 

Grade:12th pass

1 Answers

Yuvraj Singh
askIITians Faculty 75 Points
23 days ago
Que: if omega(w) is the cube root of unity then(1-w-w^2)^4 is?

Ans:
Sincewis the imaginary cube root of unity
w3=1and
1+w+w2=0...(i)
Hence
(1+w−w2)7

=((1+w)−w2)7

=(−w2−w2)7...from i

=(−2w2)7

=−128w14

=−128w12.w2

=−128(w3)4.w2

=−128w2...sincew3=1.


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