if 1 w w 2 are cube roots of unity prove the following
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Knowing the basic identities
ω3=1...(a)ω2+ω+1=0...(b)
Following can be derived from (b)
1+ω2=−ω1+ω=−ω2
Now put them in your question
=(1+ω2−w)(1−ω2+w)
=(−ω−ω)(−ω2−ω2)
=(−2ω)(−2ω2)
=4ω3
=4(1)
=4
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