complex numbers (1 Viewer)

[Koroneos]

Can someone explain to me why:

If are the nth roots of unity, then

 

[scardizzle]

well w1,w2...wn are all roots of the equation z^n = 1
using the sum of roots, we know that w1 + w2 +...wn = -b/a
in this case b = 0 hence w1 + w2 +...+wn = 0
(sorry for the lack of latex i cbf to learn at this point in time)

 

[Affinity]

Can someone explain to me why:

If are the nth roots of unity, then

slightly more elementary:

and since is not 0, you know that the sum is 0

 

[annabackwards]

An alternative method:
Since Wn is a root of z^n = 1
Then Wn=1
Wn-1 = 0
(w-1)(1+w2+w3+w4+.....+wn) = 0
Since w=/=1 then 1+w2+w3+w4+.....+wn = 0

 

[cutemouse]

Since w =/= 0

Uhh no.

 

[annabackwards]

Uhh no.

Oh yes, it shouls say "Since w=/=1"

Post edited, thanks for the pick up!

 

[adomad]

is it cause all the vectors cancel out?

 

[Flying_Penis]

is it cause all the vectors cancel out?

Retard, its because sum of roots = 0. Jesus christ you make me sick.