1. Roots of unity

Hello guys...we know that the roots of unity are for that example z^n=1 possible just for n = all positive numbers
what would happen if n = 0 or any non positive number?

thanks

2. Re: Roots of unity

Originally Posted by domenfrandolic
Hello guys...we know that the roots of unity are for that example z^n=1 possible just for n = all positive numbers
what would happen if n = 0 or any non positive number?

thanks

$\displaystyle z^{-n}=\frac{1}{z^n}$

3. Re: Roots of unity

Originally Posted by domenfrandolic
Hello guys...we know that the roots of unity are for that example z^n=1 possible just for n = all positive numbers
what would happen if n = 0 or any non positive number?
First, realize that n is an integer.

Second, if $\displaystyle n=0$ then $\displaystyle \frac{1}{n}$ is not defined. So that is take n care of.

Third, if $\displaystyle n\in\mathbb{Z}^-$ we deal the nth root of the multiplicative inverse.

4. Re: Roots of unity

hm...ok that makes sense that it comes to be 1/z^n=1...but like what happens then?how do i find solutions?are the same rools of the roots of unity applied?will we have for z^n=1 where n=-3 as an example three answers in a unit circle?
thanks

5. Re: Roots of unity

Originally Posted by domenfrandolic
hm...ok that makes sense that it comes to be 1/z^n=1...but like what happens then?how do i find solutions?are the same rools of the roots of unity applied?will we have for z^n=1 where n=-3 as an example three answers in a unit circle?
thanks
1/z^n=1 <==> z^n=1