## Proving with Discrete fourier transform with roots of unity

Hi,

I am new to this forum .. But i have a encounter numerous problems.

For for my assessment, i am required to find out the roots of unity and then find out the relationship between the length from one root to the other roots of the equation z^n = 1 and also z^n =i .

As soon as i saw this question, i immediately knew it has something to do with the "discrete fourier transform". For the conjecture i have got at the moment that could describe the relationship between the power of z (n) and the length from one root to the adjacent root is 2 sin (pi/n). What i am trying to do is to prove my conjecture that for any value of n, this conjecture will still be true with the use of discrete fourier transform.. I am not quite sure if this could be done, and if so, how can you prove the conjecture with the use of discrete fourier transform?