expected output from log of negative number

[heimdal at aracnet.com]

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: rob at utk.edu
> 
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Hi Rob,

Interesting. Could you recommend a book?

Scientia est potentia,

John