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Question

If 1,W,W2 are the cubs roots of unity then w2(1+W)3(1+W2)W=

A
1
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B
1
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C
i
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D
0
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Solution

The correct option is D 0
Given, 1,ω,ω2 are the cube roots of unity.
1+ω+ω2=0(1)
Now, ω2(1+ω)3(1+ω2)ω
=ω2(ω2)3(ω)ω[from(1)]
ω2.ω6+ω2
=ω2.(ω3)2+ω2
=ω2.1+ω2[ω3=1]=ω2+ω2=0 Ans.

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