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Question

If ω is a cube root of unity then the value of (1-ω+ω2)5+(1+ω-ω2)5 is


A

30

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B

32

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C

2

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D

None of these

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Solution

The correct option is B

32


Explanation for the correct option

Step 1: Prerequisites for the solution

Given that ω is a complex cube root of unity then we know that

ω3=1and1+ω+ω2=0

From this we have

1+ω2=-ω11+ω=-ω22

Step 2: Calculation for the correct option

As the given expression is (1-ω+ω2)5+(1+ω-ω2)5 then from the equation 1and2 we have,

1-ω+ω25+1+ω-ω25=-ω-ω5+-ω2-ω25=-2ω5+-2ω25=-32ω5-32ω10=-32ω3·ω2-32ω33·ω=-32ω2+ω=-32-1=32

Hence, the correct option is (B).


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