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Strangely enough, if you take i (the imaginary number, the square root of -1) and raise it to its own power (i.e., compute i^i), the result is actually a real number. Because exp(i*pi/2)=i (you can derive this from the fact that exp(i*pi)=-1, among other ways), i^i=exp(i*pi/2*i)=exp(-pi/2), since i*i=-1. So the imaginary parts all cancel out, and you're left with exp(-pi/2), which is approximately 0.20787957635.

Update: February 25, 2001. krimson has corrected me (via /msg), pointing out that the value of i^i is not, in fact, unique. Since i=exp(i*(pi/2+2*pi*k)) for any integer k, i^i=exp(-(2*pi*k+pi/2)) for any integer k, yielding infinitely many solutions. They're all real numbers, mind you, so the cool thing still holds true, but the value isn't well-defined in the sense of being unique. I don't think this should trouble us too much; after all, all kinds of weird things happen when you raise certain kinds of numbers to weird powers. Like raising a negative number to an irrational power... not a pretty sight! So stuff like this happens. Hey, math is cool.

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