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if w is a complex cube root of unity and (1+w^2)^n=(1+w^4)^n, then the least positive value of n

if w is a complex cube root of unity and (1+w^2)^n=(1+w^4)^n, then the least positive value of n

Grade:12

2 Answers

Akash Kumar Dutta
98 Points
8 years ago

Dear Prakhar,

we know 1+w^2=  -w

also  1+w^4=1+w^3.w=1+w=  -w^2

applying this the equation becomes:-

(-w)^n=(-w^2)^n

w^n=w^2n

w^n=1
n=3 (ANS).

Hope i helped you.

Regads.

Abhishekh kumar sharma
34 Points
8 years ago

n=3

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