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Re: expected output from log of negative number
From: |
Rob Mahurin |
Subject: |
Re: expected output from log of negative number |
Date: |
Fri, 13 Jun 2008 17:38:57 -0400 |
On Jun 13, 2008, at 2:40 PM, E. Joshua Rigler wrote:
If I type log10(-1), I get a complex number back whose real part is
the log of the absolute value of the argument, and whose imaginary
part is always equal to 1.36438. What's more, I get similar
behavior with a natural log, but the imaginary part is always equal
to Pi.
If you want exp(ln(x)) == x for negative x, you need this behavior.
You can play with Taylor expansions to see that
exp(ix) = cos(x)+i*sin(x)
(look for "Euler equation"), and so
exp(i*pi) = -1,
which suggests
i*pi = ln(-1).
Some people are intrigued that -i*pi, 2i*pi, etc. work just as well.
Intrigued enough to write books.
Cheers,
Rob
--
Rob Mahurin
Dept. of Physics & Astronomy
University of Tennessee phone: 865 207 2594
Knoxville, TN 37996 email: address@hidden