Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 exptools 1/6/84; site ihlts.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!houxm!ihnp4!ihlts!rjnoe From: rjnoe@ihlts.UUCP (Roger Noe @ N41:48:31, W88:07:13) Newsgroups: net.math Subject: Re: what is i raised to the ith power? Message-ID: <353@ihlts.UUCP> Date: Fri, 10-Feb-84 10:31:15 EST Article-I.D.: ihlts.353 Posted: Fri Feb 10 10:31:15 1984 Date-Received: Sat, 11-Feb-84 08:01:57 EST References: <680@linus.UUCP> <5043@umcp-cs.UUCP> Organization: AT&T Bell Labs, Naperville, IL Lines: 7 No! There are an infinite number of values for i^i. Any complex number C can be written as (a+bi)=C for unique reals a and b, but it can also be written in polar form with the argument indeterminate except to multiples of 2*PI. Somewhere along the line you have to take the natural logarithm of i, which is (2n+.5)i*PI for all integers n. exp(-PI/2) is in fact the principal value of i^i but all its values are given by exp(-PI*(2n+.5)). Roger Noe ihnp4!ihlts!rjnoe