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Path: utzoo!linus!decvax!mcnc!akt
From: akt@mcnc.UUCP (Amit Thakur)
Newsgroups: net.math
Subject: Re: References on i ** i, "principal logs"
Message-ID: <1960@mcnc.UUCP>
Date: Sun, 19-Feb-84 04:01:35 EST
Article-I.D.: mcnc.1960
Posted: Sun Feb 19 04:01:35 1984
Date-Received: Sun, 19-Feb-84 19:58:56 EST
References: <205@pucc-i>
Organization: Microelectronics Ctr. of NC; RTP, NC
Lines: 15


all this talk of i^i has got me wondering overtime:

i^2=(-1) a real number
ln(i)=ln|i|+i(pi/2 + 2*n*pi)= 0 + i(pi/2 + 2n*pi)
ln(a^b) = b*ln(a)
then does it follow that ln(-1)=ln(i^2)= 2i(pi/2 + 2n*pi)= i*pi(1+4n)??
in general, ln(x), x real and x < 0, then ln(x)= i*pi(1+4n) + ln(|x|)
this would mean that we could take logarithms of negative numbers.
has anyone ever thought of this before?
if this is valid, then the only number for which ln(x) is not defined
is x=0.

akt at ...decvax!mcnc!akt