# Math Proof

• Mar 11th 2009, 07:29 PM
colbys_11
Math Proof
One of my teaches gave me this problem as extra credit. Proofs like this were not a pre-requisit 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
• Mar 12th 2009, 03:57 AM
Opalg
These results are both true, but to prove them you probably need to know something about complex numbers. For the first problem, $\sin(\omega t + \tfrac{2\pi}Nk)$ is the imaginary part of $e^{i\omega t}z$, 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 $\sin^2\theta = \tfrac12(1-\cos(2\theta))$. 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).
• Mar 12th 2009, 06:56 PM
colbys_11
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
• Mar 12th 2009, 08:17 PM
colbys_11
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