Complex numbers and polynomial

[davon806]

Homework Statement

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

Homework Equations

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

 

[Mark44]

Homework Statement

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

Homework Equations

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
View attachment 90194
Thanks

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.

 

[davon806]

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

 

[Mark44]

The effect would be the same, I think.

 

[Ray Vickson]

Homework Statement

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

Homework Equations

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
View attachment 90194
Thanks

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?