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Is it possible to take the ith root of some number?

  1. Aug 29, 2010 #1
    And if so, could I take the ith root of i?
  2. jcsd
  3. Aug 29, 2010 #2
    [tex]i^{1/i}=i^{-i}=e^{-i\log i}=e^{-i\log e^{i(\pi/2+2k\pi)}}=e^{-ii(\pi/2+2k\pi)}=e^{(\pi/2+2k\pi)}[/tex]

    i has infinitely many ith roots, and they are all real!
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