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Topic: google of log(-1) (Read 5508 times) |
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william wu
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google of log(-1)
« on: Dec 10th, 2003, 10:26am » |
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When I type "log(-1)" into google, the google calculator spits out:
log(-1) = 1.36437635 i
I was wondering how google computes this. I think the answer should be [pi] i, using the formula:
ln(z) = ln(|z|) + i arg(z)
where z is a complex number. In this case, z = -1 = ei[pi]. This is a vector with magnitude one and phase [pi]. Thus, we should get
ln(-1) = ln(1) + i([pi]) = [pi]i
I already asked the google people via e-mail about this a month ago, and I got some clerky response along the lines of we can't discuss how google computes results, but we forwarded this to our engineering team since this result may not be correct (and they haven't corresponded since). Maybe someone here can make sense out of 1.36437635 i ?
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| « Last Edit: Dec 10th, 2003, 10:27am by william wu » |
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TenaliRaman
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Re: google of log(-1)
« Reply #1 on: Dec 10th, 2003, 12:06pm » |
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check the bases!
log(-1)
= log10(-1)
= log10(ei*pi)
=i*pi*log10(e)
=1.364376354*i
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towr
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Re: google of log(-1)
« Reply #2 on: Dec 10th, 2003, 12:46pm » |
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yep..
To the general public log is the 10log
While around here it's generally considered the same as ln, the natural logarithm.. It can cause a lot of confusion if you're not carefull..
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TenaliRaman
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Re: google of log(-1)
« Reply #3 on: Dec 10th, 2003, 1:09pm » |
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Actually even my scientific calculator follows the same (log as base 10 and ln as base e), so i always thought that it was a general notion.
However in mathematics log or ln is interchangeably used and assumed to be natural logarithm unless otherwise specified.(very similar to how x in sin(x) is assumed to be radians unless otherwise specified that it is in degrees).
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