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# FP2 - Roots of Unity watch

1. The question is is a cube root of 1, state the three values of x in the range -pi < x < pi and find the possible values of

For the possible values of x, I have got 2pi/3, -2pi/3 and 0. I also know that 1 + w + w^2 = 0 although I don't know how to move from there.

2. (Original post by Quido)
The question is is a cube root of 1, state the three values of x in the range -pi < x < pi and find the value of
Should that be ?
3. (Original post by Quido)
The question is is a cube root of 1, state the three values of x in the range -pi < x < pi and find the value of

For the possible values of x, I have got 2pi/3, -2pi/3 and 0. I also know that 1 + w + w^2 = 0 although I don't know how to move from there.

"The" value of ?? It gives 2 different ones depending on which you pick, unless you meant this part to be something different.
4. (Original post by atsruser)
Should that be ?
Nope, the 6 is outside the bracket unless it is a misprint
5. (Original post by RDKGames)
"The" value of ?? It gives 2 different ones depending on which you pick, unless you meant this part to be something different.
Sorry, I was meant to write the possible values of (1 - w)^6
Changed now.
6. (Original post by Quido)
Sorry, I was meant to write the possible values of (1 - w)^6
Changed now.
Ah that's better.

Okay so is given by for

Then you just consider each case separately.

For it would be useful to express this in cartesian form first before expressing it in the form then raising this to the 6th power.
7. Well, one value for (1-w)^6 should be easy...

For the others, draw 1-w on an argand diagram. Some basic geometry should let you express 1-w in form without too much work.
8. PS: if you want to do it without an Argand diagram, I think you'll find life a bit easier if you observe that

and the term in brackets can be rewritten as -2i sin(x/2).
9. (Original post by DFranklin)

and the term in brackets can be rewritten as -2i sin(ix/2).
Typo?
10. (Original post by RDKGames)
Typo?
Well, brain-fart...
11. Alright, I've got it now. Thanks everyone!

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