agd@houem.UUCP (A.DEACON) (02/10/84)
I tried to send this solution to you Mike but I don't think it made it. Jim's answer was only partially correct. The complex exponential is a multi-valued function, so i^i is also multi-valued. The values of i^i are: i -(4n+1)*pi/2 i = e n=...,-2,-1,0,1,2,3... a (set) of real numbers! Note that for n=0, we get Jim's result. The error in Jim's solution is in the step where he says i = exp(0 +pi/2) ==> .... The argument (arg) for a complex number is not unique. Pi/2 is the principle arg but you must add 2n*pi for all positive and negative n. If you insert this factor in Jim's proof, you will end up with the proper answer. Art Deacon AT&T Bell Laboratories.