1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook