
Math Proof
One of my teaches gave me this problem as extra credit. Proofs like this were not a prerequisit for the class so I dont' think he expected anyone to solve it. I don't even know where to get started and when I asked him for a suggestion of where to start he simply replied that he didnt' even know how to do it. Any suggestions of where to start would be helpful.
Here is the problem. I scanned it and cropped it so it wasn't to big.
http://img27.imageshack.us/img27/773...creditclip.jpg

These results are both true, but to prove them you probably need to know something about complex numbers. For the first problem, $\displaystyle \sin(\omega t + \tfrac{2\pi}Nk)$ is the imaginary part of $\displaystyle e^{i\omega t}z$, where z is an Nth root of unity. The result follows from the fact the sum of the Nth roots of unity is 0. This is a good place to start looking for information on this.
For the second problem, use the trig formula $\displaystyle \sin^2\theta = \tfrac12(1\cos(2\theta))$. That will transform the second problem into something looking very much like the first problem (but with cos instead of sin, and 2k instead of k).

I don't get it :(
So do i start by substituting that in for N?
I do understand how the second one relates to the first one with the trig formula though

So after looking at it(the first one) more i think i can simplify it a little bit to make it look like this
>N
[sin(wt)]Σsin(wt+(2Π/N)K) = 0
>k=1
so i took out the where k = 0