
#1
Feb414, 05:43 AM

P: 9

I don't understand why roots of unity are evenly distributed? Every time when we calculate roots of unity, we get one result and then plus the difference in degree, but I think this follows the rule of even distribution and I don't understand that, it is easy to be trapped in a reasoning cycle.
how to prove it using mathematics? Thank you 



#2
Feb414, 06:01 AM

HW Helper
P: 3,436

If that is the case then what you're noticing are complex conjugates, and it's very important to remember that every real polynomial that has a complex root will also have a complex conjugate root. But if you're actually looking for a reason why the roots of unity are all evenly spaced around the unit circle in the complex plane, then read up about De Moivre's theorem and notice that if [tex]z^n=1[/tex] where [tex]1=e^{2\pi k i}[/tex] with k being any integer, or if you're working with the trigonometric form, [tex]1=\cos({2\pi k})+i\sin({2\pi k})[/tex] and now just take the n^{th} root of both sides. It then shouldn't be hard to notice how they're evenly spaced. 


Register to reply 
Related Discussions  
Roots of unity  Precalculus Mathematics Homework  18  
Sum of nth roots of unity  Precalculus Mathematics Homework  3  
roots of unity  Calculus & Beyond Homework  1  
Roots of Unity  Calculus & Beyond Homework  1  
nth roots of unity  Calculus & Beyond Homework  1 