Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site houem.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!houxm!houem!agd From: agd@houem.UUCP (A.DEACON) Newsgroups: net.math Subject: i to the i Message-ID: <223@houem.UUCP> Date: Fri, 10-Feb-84 09:08:07 EST Article-I.D.: houem.223 Posted: Fri Feb 10 09:08:07 1984 Date-Received: Sat, 11-Feb-84 08:10:15 EST Organization: Bell Labs, Holmdel NJ Lines: 28 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.