expected output from log of negative number

[Rob Mahurin]

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