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From: ags@pucc-i (Seaman)
Newsgroups: net.math
Subject: Re: what is i raised to the ith power?
Message-ID: <192@pucc-i>
Date: Fri, 10-Feb-84 10:42:57 EST
Article-I.D.: pucc-i.192
Posted: Fri Feb 10 10:42:57 1984
Date-Received: Sun, 12-Feb-84 09:30:14 EST
References: <680@linus.UUCP> <5043@umcp-cs.UUCP>
Organization: Purdue University Computing Center
Lines: 19

The value of i ** i is not well defined.  Obviously, it must be equal
to exp(i * log(i)), but there is a problem in defining log(i).

Since exp((2*n+0.5)*i*PI) = i for any integer n, there are infinitely
many candidates for log(i).  It may seem reasonable to single out
PI/2 as THE logarithm of i, but it is a well-known fact that the
log function cannot be extended continuously to the entire complex 
plane, as a single-valued function.

What is (-1) ** i?  How about (-i) ** i?  However you define the log
function, you find yourself getting into trouble.

-- 

Dave Seaman
..!pur-ee!pucc-i:ags

"Against people who give vent to their loquacity 
by extraneous bombastic circumlocution."