[TI-M] Re: Logs of negative values
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[TI-M] Re: Logs of negative values
This might help.
http://forum.swarthmore.edu/dr.math/problems/langlands.9.15.96.html
I explains what the logarithm of a complex number is, so since the negative
reals are a subset of the complexes, this should adequately answer your
question :)
- JayEll
In a message dated 5/12/01 5:44:37 PM Mountain Daylight Time,
noveck@pluto.njcc.com writes:
> Think I'll start a new thread and see if I can get an answer to something
> that I've been wondering for a long time. . .
>
> I've noticed that if an 89/92+ is set with the complex mode to rectangular
> or polar, then it will return an imaginary answer when you try to take a log
> (any base?) of a negative number.
>
> For example, ln(-1) returns PI*i.
>
> I've been taking AP Calc AB this year, and I've yet to see anything about
> taking logs of negative numbers. My precalc teacher last year insisted that
> it's absolutely impossible to do so -- she didn't say anything along the
> lines of it being impossible for us with our knowledge; she said it was
> outright impossible. When I showed her the calc doing it, she had no clue
> what it was doing.
>
> I was surprised; I would expect that if someone is teaching math, they
> should at least understand concepts beyond their own knowledge. Then again,
> since we Americans barely pay our teachers enough to make a living, they
> typically weren't the smartest ones back when they were in school.
>
> So I was wondering two things: at what level of math is this taught, and, if
> the concept is simple enough, could someone explain it?
>
> I think it's related to the formula e^(x*i) = cos(x)-i*sin(x), which I've
> seen online many times before but that I've yet to reach (does it come up
> with Taylor series? I've seen it derived in context with them). Anyways, a
> little enlightenment would be appreciated =)
>