# nth roots of unity

• Dec 1st 2010, 06:08 AM
MattWT
nth roots of unity
Hello again,

Suppose, you had to find the 5th roots of unity for 1, in polar form.

This is how far i'm getting.

You would say in the argand plane, 1 would make an angle of 0 to the horizontal and you would take r as being 1.

Then you would say

$z = 1e^(i(0 + 2*pi*k))$
$z = e^(i(2*pi*k))$

Apologises for the mess above, can't seem to figure out power brackets on this, it's all to the power of e ^

Then for each k, from 0 to 4, you would place into this formulae to get the 8 roots?

Thanks again!
• Dec 1st 2010, 06:50 AM
Plato
The n nth roots of unity are; $\displaystyle e^{\frac{2k\pi i}{n}},~~k=0,1,\cdots,n-1$.