Thread: 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

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

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 then is not defined. So that is take n care of.

Third, if we deal the nth root of the multiplicative inverse.

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

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