Here is the problem:

Let P sub 0, ....., P sub n-1 be n equally spaced points on the unit circle. Compute the product of the distances from P sub 0 (naught) to all the remaining points.

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- April 6th 2007, 11:49 AMchadlyterProducts of the unit circle
Here is the problem:

Let P sub 0, ....., P sub n-1 be n equally spaced points on the unit circle. Compute the product of the distances from P sub 0 (naught) to all the remaining points. - April 6th 2007, 12:31 PMThePerfectHacker
- April 6th 2007, 12:42 PMPlato
This is my understanding.

http://img66.imageshack.us/img66/7773/rootsumpx7.gif - April 6th 2007, 02:35 PMThePerfectHacker
- April 6th 2007, 03:43 PMPlato
- April 8th 2007, 08:51 AMThePerfectHacker
- April 8th 2007, 09:53 AMThePerfectHacker
I am going in unit circles (get the pun) with this problem.

But I managed to make this problem more complicated than it should be. Instead of working with cyclotonomic polynomials, as I should have. I reduced the problem to trigonometry which makes it more difficult.

I am sure you know what I am about to say but let me just post it.

A**cyclotonomic polynomial**is,

\Phi_n(z) = 1+z+z^2+...+z^n

We can factor them as,

(z-z_1)(z-z_2)+...+(z-_n)

Where,

z_1,z_2,...,z_n

Are points on the regular (n+1)-gon inscribed in the unit circle in the complex plane (except unity).

Basically, I am saying this is the cyclotonomic polynomial of degree n evaluated at 1.