Complex Numbers-roots of unity (1 Viewer)

[Bozza555]

Could someone explain how to work these sort of questions out please? even when i look at the answers i don't understand haha

<a href="http://www.codecogs.com/eqnedit.php?latex=if~ \omega ~ is~a~complex~cube~root~of~unity,show~that~ (1@plus;\omega )^3(1@plus;2\omega@plus;2\omega^2)=1" target="_blank"><img src="http://latex.codecogs.com/gif.latex?if~ \omega ~ is~a~complex~cube~root~of~unity,show~that~ (1+\omega )^3(1+2\omega+2\omega^2)=1" title="if~ \omega ~ is~a~complex~cube~root~of~unity,show~that~ (1+\omega )^3(1+2\omega+2\omega^2)=1" /></a>

 

[nightweaver066]

Since w is a complex cube root of unity, w satisfies z^3 = 1

So w^3 = 1

w^3 - 1 = 0

(w -1)(w^2 + w + 1) = 0

But w is complex, so w^2 + w + 1 = 0

Using this for that question,











Basically for these sorts of questions, keep using w^3 = 1 and w^2 + w + 1 = 0 to get a nice, simple answer.

 

[Bozza555]

ohh i get it now, i wasn't sure why w^2+w+1=0 and why it couldn't be w-1=0 but i forgot that w is complex
thanks