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

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.

n=3