Grade 11Algebra
If 1, w and w^2 is cube root of unity then show (1-w+w^2)(1-w^2+w^4)(1-w^4+w^8)......to n factors=2^2n.
1 Answer
Shailendra Kumar Sharma
as we know 1-w+w2= 0
so 1+w2 =-w, so it will be -2w
take 1-w2+w4
=1-w2+w3*w=1-w2+w
(-w2-w2)=-2w2
Next term is 1-w4+w8 =( 1-w+w2)
so the trend will repeat
Now (1-w+w2)X1-w2+w4 =(-2w)*(-2w2) =2^2
similarly for n terms it will be 2^2n
so 1+w2 =-w, so it will be -2w
take 1-w2+w4
=1-w2+w3*w=1-w2+w
(-w2-w2)=-2w2
Next term is 1-w4+w8 =( 1-w+w2)
so the trend will repeat
Now (1-w+w2)X1-w2+w4 =(-2w)*(-2w2) =2^2
similarly for n terms it will be 2^2n
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