Omega - Q8 2003 (1 Viewer)

[Premus]

Hey

I have no idea how to do q8 part a) i) .... from the 2003 HSC
is there a special way to approach questions having omega?... i dont think i understand the basis behind this??

also...what other types of questions could come, related to omega?

Thanks a lot!

 

[ngai]

is there a special way to approach questions having omega?

use w^3 = 1
and use w^3 = 1
and use w^3 = 1 again
and keep using w^3 = 1

 

[withoutaface]

suppose you have something like w³=1

then there are three possible roots of the equation z³=1

z= 1, w, w²(because w⁶=(w³)²=1²=1)

so you can say stuff like 1+w+w²=0 (sum of the roots) and use that.

</random notes>

 

[Premus]

ummmm

w^3 = 1 and we need to find the values for 1 + w ^k + w^2k

....sorry im really confused..not sure what the question is actually asking... where can i substitute w^3 = 1 ??

Thanks for ur help!

 

[ngai]

well, w^k is either 1, cis(2pi/3), or cis(-2pi/3)
so sub them all in

 

[withoutaface]

ummmm

w^3 = 1 and we need to find the values for 1 + w ^k + w^2k

....sorry im really confused..not sure what the question is actually asking... where can i substitute w^3 = 1 ??

Thanks for ur help!

look at my post, you use the sum of the roots for the equation z³-1=0

 

[Archman]

1 + w = -w^2 is good too.
so is 1 + w^2 = -w (you'll be surprised how many people miss these)

 

[withoutaface]

1 + w = -w^2 is good too.
so is 1 + w^2 = -w (you'll be surprised how many people miss these)

If they can't see those they shouldn't be doing 4u