Yet another Cube Roots of Unity Question... (1 Viewer)

[cutemouse]

Hi,

Here's the question, I have no idea on how to do it.

If 1, ω, ω² are the 3 cube roots of unity, prove that

(a+bω+cω²)/(b+cω+aω²)= ω

Thanks,

Jason

 

[namburger]

LHS:
(a+bω+cω^2)/(b+cω+aω^2)
= (aω^3+bω+cω^2)/(b+cω+aω^2)
as ω^3 = 1
= ω(aω^2+b+cω)/(b+cω+aω^2)
= ω

 

[kooltrainer]

too goood

 

[cutemouse]

Geez that was simple ... Thank you!!