Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site pucc-i Path: utzoo!linus!philabs!cmcl2!floyd!harpo!ihnp4!inuxc!pur-ee!CS-Mordred!Pucc-H:Pucc-I:ags 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."