Re: TI-85 and log(-4)

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: TI-85 and log(-4)
From: Geoff Hagopian <galois@cyberg8t.com>
Date: Fri, 25 Jul 1997 14:16:51 -0700
Organization: College of the Desert
References: <Pine.SOL.3.91.970725105842.3510B-100000@email2.asu.edu>
Reply-To: galois@cyberg8t.com

Geez, are you tossing out a softball?  I'll swing.

If you're willing to accept Euler's formula: e^(ix)=cos(x)+i*sin(x).
(It require an understanding of analytic continuation - see Taylor
series)
Then by generalizing the definition of the natural logarithm, ix =
ln(cosx+isinx).
So for instance, if x = pi, the i*pi = ln(-1) gives you some
justification of how
the logarithm of a negative will be complex valued.

This stuff gets glossed over alot in most curricula.  There's a course
called
complex analysis you can take after you pass real analysis which comes
sometime
after the calculus sequence.

geoff h

> On Thu, 24 Jul 1997, David Socher wrote:
>
> > My algebra instructor had everyone punch the log of a negative
> number
> > into their calculator to demonstrate that this could not be done.
> > Everyone got an error message except me and my TI-85.  I got
> something
> > that looks like a complex number.  My instructor couldn't explain
> it.
> > The manual doesn't to cover it.  Can anyone tell me what's happening
>
> > here?

References:

Re: TI-85 and log(-4)

From: Jesse Samuels <JESSE.SAMUELS@ASU.EDU>