complex numbers need help as usual (1 Viewer)

[blackfriday]

here's the question of the week:

if w is a complex cube root of unity, evaluate a+bw+cw^2/b+cw+aw^2 where a, b and c are real numbers.

much help appreciated

 

[Euler]

multiply top and bottom by w, you get w as the answer.

 

[blackfriday]

doesnt really help me because i cant get it. well i was sick today and couldnt get a single volumes question right.

 

[Euler]

hmmm...ok.
if w is a cube root of unity, then you know that w^3=1.

then for (a+bw+cw^2) / (b+cw+aw^2), multiply top and bottom by w...you get
w(a+bw+cw^2) / w(b+cw+aw^2)

the denominator expands to give a+bw+cw^2 which cancels out with the top, leaving you with just w.

 

[blackfriday]

*smacks head on wall*

thanks!

 

[mojako]

here's the question of the week:

if w is a complex cube root of unity, evaluate a+bw+cw^2/b+cw+aw^2 where a, b and c are real numbers.

much help appreciated

question of the week?
does that mean you can't ask another question this week??

 

[funk_master81]

yeah Euler is right on the money. I would have been able to answer that no probs

 

[blackfriday]

question of the week?
does that mean you can't ask another question this week??

no that was my 'intellectual' challenge of the week