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

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The discussion confirms that it is possible to take the ith root of the imaginary unit i. The calculation shows that i raised to the power of 1/i equals e raised to the power of -i log(i), leading to the conclusion that i has infinitely many ith roots, all of which are real numbers. This result is derived using complex logarithms and Euler's formula, specifically e^{(\pi/2 + 2k\pi)} for integer values of k.

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And if so, could I take the ith root of i?
 
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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)}

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

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