root of unity question? (1 Viewer)

[leisl1990]

i was just looking at the solution of a past paper question.

if w^n=1

1+w^1+w^2+.......w^(n-1)=1

true? and why?

 

[Affinity]

it's false.. the sum is either 0 or n.

[1-w][1+w^1+w^2+.......w^(n-1)] = 1-w^n = 0

so if w is not 1, then 1-w is not 0 so [1+w^1+w^2+.......w^(n-1)] must be 0,
else the sum is n.

 

[leisl1990]

it's false.. the sum is either 0 or n.

[1-w][1+w^1+w^2+.......w^(n-1)] = w^n - 1 = 0

so if w is not 1, then 1-w is not 0 so [1+w^1+w^2+.......w^(n-1)] must be 0,
else the sum is n.

good. thanks so much..