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Question

If ω(1) is a complex cube root of unity and (1+ω4)n=(1+ω8)n, then the least positive integral value of n is ?

A
2
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B
3
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C
6
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D
12
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Solution

The correct option is A 3
(1+ω4)n=(1+ω8)n

(1+ω)n=(1+ω2)n

(ω2)n=(ω)nω2n=ωn

For n=2

(ω2)2=ωω2

For n=3

ω6=ω3=1

Least value of n is 3

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