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Prove that (1+w)^3 - (1+w^2)^3=0 Here W is cube root of unity Please provide the whole proof 😊😊.

Prove that (1+w)^3 - (1+w^2)^3=0 Here W is cube root of unity Please provide the whole proof 😊😊.

Grade:11

1 Answers

Arun
25757 Points
5 years ago
Dear Piyush
Β 
As we know
1 + w + w2Β = 0
hence we can writeΒ 
1 + w = – w2Β  andΒ  1 + w2Β = –wΒ  and w3Β = 1Β  Β  Β  when required
Β 
Now
(1 + w)3 – (1 + w2)3
( – w2)3 – ( –w)3
 – w6Β + w3
Β  – 1 + 1
Β = 0
Β = RHS
Hence Proved
Β 
Regards
Arun (askIITians forum expert)

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