If 1,ωandω2are the cube roots of unity, 3+ω2+ω46 is equal to
64
729
2
0
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.