If 1 2 , w, w are the cube roots of unity, then prove the following :(1+w) (1+w^2 ) (1+w^7 ) (1 +w^*8)=1
Akash Chauhan , 7 Years ago
Grade 12
Algebra> If 1 2 , w, w are the cube roots of unity...
1 Answers
Ritesh Khatri
Last Activity: 7 Years ago
we know that w3 = 1
and 1 + w + w2 = 0
therefore w7 = w
and w8 = w2
given expression becomes
(1+w)2 (1+w2 )2
=[(1+w) (1+w2 )]2
=(1 + w3 + w + w2)2
=(1 + 0 )2
=1
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