Re: complex #'s

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: complex #'s
From: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>
Date: Thu, 23 Apr 1998 11:51:31 -0400
Reply-To: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>
Glen Nowak writes:

>  on the TI86 when ever you get an complex # as an answer it displays it
>  like an ordered pair but that isnt what my teacher wants she wants it
>  in the form a+bi can anyone tell me if you can put the answers into
>  that form on the 86

It's purely a matter of notational convention.  The a+bi or a+bj format is more
common in elementary and intermediate mathematical work, the ordered-pair
format (a,b) more common in engineering contexts (so I understand).  The
advantage of the latter is that you don't need a special key in order to enter
complex numbers.  The advantage of the former is that it doesn't _look_ like an
ordered pair, which is why it is more commonly used in introductory work.  But
it has its own disadvantages.

In the college-level-algebra-etc. course I teach, most of the students have
TI-83's, and the textbook author uses a+bi, so we have a good match. The few
students who use TI-86's simply have to switch mental gears when we get to
working with complex numbers -- not really a problem for them, and no problem
for me!

Theoretically TI could have set up two different modes to allow users their
choice of format, but it probably would have added a buck or two to the cost of
the calculator, not to mention a layer of complexity that most users didn't
need.  I think they made a wise choice.

Notational conflicts are always with us in mathematics.  The notation for
_lists_ on all of the TI-8x's is the same as standard listing notation for
_sets_, a quite different concept.  But how many different-shaped brackets do
you want to have to deal with?

Let's be glad no-one ever thought of trying to get the calculator to accept the
old square-root-of-minus-one notation!  Oh, and by the way, there's another
whole battle fought between mathematicians and engineers over appropriate
notation for complex numbers in _polar_ form.  And should we be working in
degrees or radians, and all that.  Talk about religious wars....

RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623

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