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Question

(a+bω+cω2c+aω+bω2)+(a+bω+cω2b+cω+aω2)

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Solution

As we know that ω3=1,1+ω+ω2=0
(a+bω+cω2c+aω+bω2)+(a+bω+cω2b+cω+aω2)= (aω3+bω4+cω2c+aω+bω2)+(aω3+bω+cω2b+cω+aω2)=(ω2)×(c+aω+bω2c+aω+bω2)+(ω)×(b+cω+aω2b+cω+aω2)=ω+ω2=1

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