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Question

If ω and ω2 are cube roots of unity, prove that (2ω+2ω2)(2+2ωω2)=9

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Solution

(2ω+2ω2)(2+2ωω2)=9
Take L.H.S
=(2ω+2ω2)(2+2ωω2)
We know 1+ω+ω2=0,ω3=1
=[2(1+ω2)ω][2(1+ω)ω2]
=[2ωω][2ω2ω2]
=(3ω)(3ω2)
=9ω2=9
Hence proved.

1097435_1137927_ans_58c4a7789e954a39a65baeb5fbb13107.jpg

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