I've been doing a lot of thinking about imaginary numbers lately. My first question was "What is sqr(i)?". I thought it was unsolvable until I punched it into my trusty (and often right) caclulator and found out it was (sqr(.5)i + sqr(.5))^2 So obvious now. Of course. Anyways, a while later, I thought about series of powers (the same way a power is a series of multiplications and those a series of additions). (We'll call a series of power ^^) So my question is: x^^2 = x^x = -4 What is x? My calculator tells me: false. But I have this tendency not to trust it sometimes, especially when it won't give me an answer. Also, is i ^ i defined? ((-1)^.5)^((-1)^.5) = (-1)^(i/2) = ?