Complex numbers and polynomial

1. Oct 14, 2015

davon806

1. The problem statement, all variables and given/known data
Hi,I have a problem regarding to one of the questions in my homework.Actually I am not trying to ask for the solution.I am just not sure what the question is asking for.Please see the attached

2. Relevant equations

3. The attempt at a solution
In 5(c),the summation notation stated that i = 1,j=1 and i<j.
Q1:If i<j,then why don't start at j =2?Coz j=1 cannot be smaller than i
Q2:What exactly does i = 1,j=1 means?I got confused with that it matrix multiplication(two summation signs).On the contrary,there is only one summation sign here.
It would be helpful if someone can expand the first few terms in the summation

Thanks

2. Oct 14, 2015

Staff: Mentor

The exponents i and j run through all integer values from 1 up through 2n + 1. The "i < j" part means, I believe, that all expressions $\omega^{i + j}$ where if i < j add up to zero. The summation would include $\omega^{1 + 2}, \omega^{1 + 3}, \omega^{1 + 4}, \dots, \omega^{2 + 3}, \omega^{2 + 4}, \dots$, and so on. The summation wouldn't include $\omega^{1 + 1}$ and several others.

3. Oct 14, 2015

davon806

So practically j = 1 should be replaced with j = 2 ?

4. Oct 14, 2015

Staff: Mentor

The effect would be the same, I think.

5. Oct 14, 2015

Ray Vickson

I agree that someone should expand the first few term in the summation---and it should be YOU that does it. How or why are you prevented from doing that?