[TI-M] Re: Logs of negative values
[Prev][Next][Index][Thread]
[TI-M] Re: Logs of negative values
If you look on a calculator besides the 89, such as the 83+, you'll notice that instead of real,
rectangular, and polar, the modes for complex numbers are real, a+b*i, and r*e^(theta*i). These
modes obviously correspond to the ones on the 89, but it is easier to see what they mean. Back to
the 89... Try typing i in while in polar mode; this returns e^(pi/2 * i). Obviously, to get
negative one in this format, you must square the two expressions. A power to a power is the
product of the powers, so -1=e^(pi*i). From this, it is obvious that ln(-1)=pi*i. This can be
used to find the logs of other negative numbers as well.
This is of course not the best way to get to this, but it's how I figured it out when I was unable
to find any explanation of this stuff.
jeff
--- Scott Noveck <noveck@pluto.njcc.com> wrote:
>
> 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
>
>
>
__________________________________________________
Do You Yahoo!?
Yahoo! Auctions - buy the things you want at great prices
http://auctions.yahoo.com/
References: