[TI-M] Logs of negative values
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[TI-M] Logs of negative values
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 =)
-Scott
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