Roots of unity (1 Viewer)

[ashokkumar]

If w is the complex cube root of unity, evaluate (1 - 3w + w^2)(1 + w + 8w^2)

 

[Trebla]

If w is the complex cube root of unity, evaluate (1 - 3w + w^2)(1 + w + 8w^2)

If w is the complex cube root of unity then
w³ = 1
=> (w - 1)(w² + w + 1) = 0
=> w² + w + 1 = 0 for non-real w
(1 - 3w+w²)(1 + w + 8w²)
= 1 + w + 8w² - 3w - 3w² - 24w³ + w² + w³ + 8w⁴
= 1 + w + 8w² - 3w - 3w² - 24 + w² + 1 + 8w
= - 22 + 6w + 6w²
= 6(w² + w) - 22
= 6(-1) - 22
= - 28

 

[ashokkumar]

oooh sorry there was a typo in the question.

its meant to be (1 - 3w + w^2)(1 + w - 8w^2).

But i understand the method now anyway. I just wanted to double check, is the answer 36?

 

[shaon0]

oooh sorry there was a typo in the question.

its meant to be (1 - 3w + w^2)(1 + w - 8w^2).

But i understand the method now anyway. I just wanted to double check, is the answer 36?

Yeah, think so.

 

[Lukybear]

36 is what ive got.