i-th root of i

In my previous post we talked about i^i and we evaluated it. We found that the result is a real number, although you would expect it to be complex since i is an imaginary number. Is this the case for the i-th root of i?

First of all, let’s write this as a power:

Now, this is can also be written as

We already know what i^i equals

therefore,

This means it’s simply the inverse of i^i, and so it’s a real number as well! If you use a calculator you will see that the result is 4.810477…

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1 Comment »

  1. ok i was searching this to see if i discovered something. but i made it (i)root(i)=square root of e to the pi. damn and i wanted to name 4.810477…..

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