Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site mcnc.UUCP 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