L leisl1990 Member Joined Feb 13, 2007 Messages 108 Gender Male HSC 2008 Oct 25, 2008 #1 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?
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 Active Member Joined Jun 9, 2003 Messages 2,062 Location Oslo Gender Undisclosed HSC 2003 Oct 25, 2008 #2 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. Last edited: Oct 25, 2008
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.
L leisl1990 Member Joined Feb 13, 2007 Messages 108 Gender Male HSC 2008 Oct 25, 2008 #3 Affinity said: 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. Click to expand... good. thanks so much..
Affinity said: 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. Click to expand... good. thanks so much..
