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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