I was researching infinite tetrations recently and thought of a super interesting, although admittedly pointless, math question regarding it. I was wondering if anyone can help me solve it.
Say we have i^i, can you take an infinite tetration of that? And more generally, can you take the infinite tetration of any complex number (a+bi)^(a+bi)? It's kinda random, but it seems pretty neat.
Just an interesting thought that I couldn't really figure out.
Thanks
Edit: Someone pointed out that "tetration" is a bit vague. What I mean is repeated exponentiation, so like the infinite tetration of x is x^x^x^x^x... so on. So I'm asking about (i^i)^(i^i)^(i^i)^(i^i)...