Hmm... maybe you'll find the solution here

baseball reference

wtf?? -_-

]]>i^i = exp(i clog(i)) = exp(i ( ln(1) + i.pi/2))) = exp(i^2. pi/2) = exp(-pi/2) = 0.2078...

]]>This is as far as I've gotten:

From that:

That said:

Also:

Which shows:

With a similar method (that is kind of tedious to do out) I found:

I get how to find the kth root of any imaginary number, but I can't make a general rule, I have to do each out by hand.

Using Taylor series I can show :

And from there I think I get k^i, but only if k is a real number.

which leaves me with the following questions:

That last one is a calculator answer, but * why? *

Any other I properties would be fun to see, so if anyone else has something to offer, please, I'd like to learn as much as I can about complex numbers.

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