# Thread: Math Proof

1. ## 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.

2. 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).

3. 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

4. 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