Roots of unity (1 Viewer)

[samuelclarke]

When we're solving for roots of unity and the power is odd (z^3=1) does that mean we use k = 0, +-1, +-2? and if the power is even (z^4=1) do we use k=0,1,2...?

 

[Carrotsticks]

Nope.

If we have something like z^3=1, then we use k=0, +-1. Each k value gives a different solution. Since we have 3 solutions, we do k=0, +-1 (3 solutions).

You has +-2 there, which would have given us repeats.

If it was z^5=1, THEN we would use k=0, +-1, +-2.

For even n, we do the usual k=0, +-1 etc etc, then we take the next positive value of k.

ie: z^4 = 1. Then we would have k=0, +-1, +2.

z^6 = 1. We would have k=0, +-1, +-2, +3.

etc etc.

 

[samuelclarke]

wait so either way the 'k' would be 0, -1, +1, -2 and so on depending upon the 'n' value in z^n?

 

[Carrotsticks]

Yep, just keep progressing with the plus/minus until we get n solutions.

 

[samuelclarke]

ok thanks!

 

[Espy25]

What if its Z^5 = -1? Do we still use k = 0, +-1 and +-2?

 

[lgnorance]

Wait, what? Can someone tell me where this k stuff comes in? Is there a general solution for solving roots of unity? HELP.

 

[jax447]

^ ignorance