I understand this but can u please expand on how dividing z^5-1 with z-1 gets the rhs? Thanks!has roots
let be w, be w conjugate and j for the other root etc.
dividing z^5 -1 with z -1 gets the RHS
same with the j root.
and then you get the result as required.
edit: don't know how to do conjugates so if anyone reading could show how to latex it i would appreciate
You can prove it through polynomial division. If you were to manually divide both polynomials, you would get that term.I understand this but can u please expand on how dividing z^5-1 with z-1 gets the rhs? Thanks!
Ahhhhh okkk makes sense now thank you!!You can prove it through polynomial division. If you were to manually divide both polynomials, you would get that term.
You could factorise z^5 - 1 into two polynomials
as you can see, all the terms in the polynomial are multiplied by z first, and then the regular polynomial is multiplied by -1 so all the terms between z^5 and -1 would be cancelled out
so when you divide by z - 1.
Not the solution to (v) but just another method for these type of questions;
I think the question would have explicitly stated to use part (iv) if they meant for you to use it. But it I guess the question was kinda building up to that point through all the previous parts, so your way would have been correct too and in timed conditions my method would take way to long for 2 marks.I understand... I was wondering whether it meant to use part (iv), or about noting that part(iv) was derived from (ii), and so using it is building from part (ii)