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Question

If ω is a complex cube root of unity, then (1ω+w2)7+(1+ωω2)7=

A
27
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B
26
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C
25
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D
24
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Solution

The correct option is A 27
(1w+w2)7+(1+ww2)7
=[(1+w2)w]7+[(1+w)w2]7
=[ww]7+[w2w2]7
=(2w)7+(2w2)7
=27(w7w14)
=27(w6.ww12.w2)
=27(ww2)
=27(1)
=27

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