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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
25763 Points
3 years ago
Dear Piyush
 
As we know
1 + w + w2 = 0
hence we can write 
1 + w = – w2  and  1 + w2 = –w  and w3 = 1      when required
 
Now
(1 + w)3 – (1 + w2)3
( – w2)3 – ( –w)3
 – w6 + w3
  – 1 + 1
 = 0
 = RHS
Hence Proved
 
Regards
Arun (askIITians forum expert)

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