proof help

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December 7th 2009, 05:07 AM
ux0

proof help

Let $\zeta = e^{2\pi i/n}$

Prove that

$x^n-1=(x-1)(x-\zeta)(x-\zeta^2)...(x-\zeta^{n-1})$

And if n is odd, that

$x^n+1=(x+1)(x+\zeta)(x+\zeta^2)...(x+\zeta^{n-1})$

If i could get help on the first part i think i should be able to do the odd part.
December 7th 2009, 05:56 AM
tonio

Quote:

Originally Posted by ux0

Let $\zeta = e^{2\pi i/n}$

Prove that

$x^n-1=(x-1)(x-\zeta)(x-\zeta^2)...(x-\zeta^{n-1})$

And if n is odd, that

$x^n+1=(x+1)(x+\zeta)(x+\zeta^2)...(x+\zeta^{n-1})$

If i could get help on the first part i think i should be able to do the odd part.

For this you need to know, or hopefully to remember, how to find n-th roots of a complex number...it's a little long to explain it here.

Tonio

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