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
Prakhar Srivastava , 11 Years ago
Grade 12
Algebra> cube-root-of-unity...
2 Answers
Akash Kumar Dutta
Last Activity: 11 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
Last Activity: 11 Years ago
n=3
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