Prove that (1+w)^3 - (1+w^2)^3=0 Here W is cube root of unity Please provide the whole proof 😊😊.
Piyush Upadhyay , 7 Years ago
Grade 11
Magical Mathematics[Interesting Approach]> Prove that (1+w)^3 - (1+w^2)^3=0 Here W i...
1 AnswersArun
Last Activity: 7 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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