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Question

If ω is an imaginary cube root of unity, then (1+ω-ω2)7 equals


A

128ω

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B

-128ω

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C

128ω2

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D

-128ω2

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Solution

The correct option is D

-128ω2


Explanation for the correct option

As we know that when ω is an imaginary cube root of unity then

ω3=1and1+ω+ω2=0 which can be rewritten as 1+ω=-ω2

Now, the given expression is (1+ω-ω2)7

1+ω-ω27=-ω2-ω27=-2ω27=-128ω14=-128ω34·ω2=-12814·ω2=-128ω2

Hence, the correct option is (D).


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