Re: IMAGINARY NUMBERS

["VERNON DEWEES" <vrdewees@tenet.edu>]

Seckinger, Jennifer wrote:
> Hello Phys-l-ers:
>
> I teach physics and 2nd year algebra to high school juniors and seniors.
> Very soon we will be encountering imaginary numbers in the algebra class.
>  Of course, the inevitable questions "Why do we have to do this?", "Who
> invented this?", and "Why will I ever need this?" will rear their ugly
> little heads!
>
> My undergraduate degree is in physics and I **VAGUELY** remember doing a
> little something with imaginary numbers in an optics class and/or e-mag.
> However, it's not enough of a memory to help me out!  If you can help me
> out, any ideas would be greatly appreciated.  The teacher's edition of
> our text points out, oh so helpfully, that imaginary numbers "have many
> important applications, particularly in engineering and electronics."
> I'm sure some of the kids won't be satisfied with that statement and
> would instead prefer to at least HEAR of a few of the particulars.  (As a
> high school student, I never CARED what they could be used for--it was
> just a fun puzzle to solve!)
>
> Thanks in advance!
> *************************************************************************
> Jennifer Seckinger                "Everything should be made as simple as
> Evansville, IN                               possible, but not simpler."
> jsecking.ucs@smtp.usi.edu                             --Albert Einstein
>
> *************************************************************************
Jennifer,

Complex numbers are all around us. Every number has a real and imaginary
part, it is just that the imaginary part's coefficient is zero for most
of the numbers we use. The place I emphasize imaginary(I really dislike
this term, but do not know a better one) numbers is alternating current
wall sockets. AC circuits have real and imaginary parts. Look in some
undergraduate circuit analysis books for Electrical Engineering. I tell
my students that is imaginary numbers did not really exist, the lights
in the room and the plugs in the wall would not work. 

I am sure Leigh, Donald, or many of the others on this list will give
you better, elequent examples and explanations.

Better yet, give someone extra credit for reporting to the class on this
topic.

Vern Dewees