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Question

If 1,ωandω2are the cube roots of unity, 3+ω2+ω46 is equal to


A

64

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B

729

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C

2

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D

0

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Solution

The correct option is A

64


Explanation of the correct option:

Step1. Define the cube root of unity.

Given,

1,ωandω2are cube root of unity.

1+ω+ω2=0____(1)Fromdefinition,ω=-1+i32,ω2=-1-i321×ω×ω2=1____(2)

Step2. Find the value of (3+ω2+ω4)6:

3+ω2+ω46=3+ω2+ω3ω6=3+ω2+ω6[From(2),ω3=1]=2+1+ω2+ω6=2+06[From(1),1+ω+ω2=0]=26=64

Hence, Option(A) is the correct answer.


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