Some math help.

[iDante]

So my math teacher gave us some extra credit. The problem is this:

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x^3 - 1 = 0
x^6 - 1 = 0
x^12 - 1 = 0
Solve for all (real and imaginary) values of xI promptly factored/solved them and showed him my answers. He said, "What you did is correct, but this can also involve trigonometry and there should be a picture involved." So I need to show him that to get the extra credit.

The answers to the first one (x^3 - 1 = 0) are this btw, if it helps:

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x = {1, (-1/2) + (sqrt(3)/2)i, (-1/2) - (sqrt(3)/2)i }
Any help is much appreciated, as I have no idea what he's going on about.

[N. Escalona]

solved on IRC, topic can be locked AFAIK

[~Niko~]

Im doing that kind of stuff at shool too

[Sir Jeremy]

I am not.  Thank God.  Looks fairly complicated.  Luckily I'm still in easy algebra. <3

[N. Escalona]

If anyone's curious, the answer is the nth roots of unity. Look it up on Wikipedia or Mathworld.

[~Niko~]

I am not.  Thank God.  Looks fairly complicated.  Luckily I'm still in easy algebra. <3

it's not complicated. I do them as if they would be sums

[blackdevil0742]

sigh. I used to be good at these but 1.5 years without math... can't even remember anything anymore.

[LtKillroy]

I have a calculator that does that for me. It makes it easier.

[iDante]

Actually it is pretty complicated. Finding the answers is easy, as LtKillroy said you can just plug it into a TI-89 and it spits out the answers.

But it turns out that when you get things with x^n = 1 then interesting things happen.

If anyone's curious, the answer is the nth roots of unity. Look it up on Wikipedia or Mathworld.

(this can be locked thanks people)

[a-4-year-old]

I have a calculator that does that for me. It makes it easier.

When you get a test that doesn't allow calculators then you're boned

[The Geologist]

Locked