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Math Help - nth roots of unity ???

  1. #1
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    nth roots of unity ???

    for which n is i an nth root of unity?

    hmm, thanks
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by dixie View Post
    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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