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Re: expected output from log of negative number
From: |
heimdal |
Subject: |
Re: expected output from log of negative number |
Date: |
Fri, 13 Jun 2008 15:26:49 -0700 |
Rob Mahurin wrote:
> 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
>
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Hi Rob,
Interesting. Could you recommend a book?
Scientia est potentia,
John