cube roots of unity question (2 Viewers)

[weeeeeed]

How did they make this conversion? (w+1)^2=(-w^2)^3

 

[SilentWaters]

The "conversion" to which you refer has been cited incorrectly. In the snapshot (Cambridge, from the font I think?) there is a cube on both sides.

What's inside the brackets on each side should be clear through a re-arrangement of . Move the squared term to the other side and violà.

 

[wiliaamnguuyen]

What does it mean, when they say 'w' is a non-real cube root of unity?
Does it mean
w is a complex number? and can't equal to 1?

Stupid question, but I need to be 110% sure about this

 

[wiliaamnguuyen]

And to answer your question, basically.
They made the conversion by using this solution from cube roots
w^3 -1 = 0
(w-1)(w^2+w+1)=0
therefore, w^2+w+1=0

And w+1 = -w^2
and yadidada

 

[ymcaec]

What does it mean, when they say 'w' is a non-real cube root of unity?
Does it mean
w is a complex number? and can't equal to 1?

Stupid question, but I need to be 110% sure about this

Yes. w has an imaginary part (thus non-real) and so it cannot be 1.
If w is 1 , then