# nth roots of unity ???

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• Jan 7th 2009, 05:46 PM
dixie
nth roots of unity ???
for which n is i an nth root of unity?

hmm, thanks
• Jan 7th 2009, 07:44 PM
Math Major
A root of unity is a complex number that yields 1 when raised to some nth root.

i is defined to be (-1)^(1/2)
i^2 then would be (-1)^(1/2)^2 = (-1)^(2/2) = (-1)^1 = -1
i^3 would be i^2 * i = -1 *i = -1
i^4 would be i^2 * i^2 = -1 * -1 = 1

Every fourth term will result in a value of 1.
• Jan 7th 2009, 07:44 PM
mr fantastic
Quote:

Originally Posted by dixie
for which n is i an nth root of unity?

hmm, thanks

The nth roots of unity are $\cos \left( \frac{2 \pi}{n}\right) + i \, \sin \left( \frac{2 \pi}{n}\right)$.

So you require the integer values of n such that $\sin \left( \frac{2 \pi}{n}\right) = 1 \, ....$
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