RE: IMAGINARY NUMBERS

["Quist, Oren Phys" <QuistO@mg.sdstate.edu>]

An example I like to use when showing the need for complex numbers
is to tell the students to find the THREE cube roots of +1.
Oren Quist, SDSU

 ----------
From:  Bob Sciamanda
Sent:  Sunday, February 01, 1998 9:25 PM
To:  QuistO; RAUBERJ; phys-l
Subject:  Re: IMAGINARY NUMBERS


Jennifer,
            This may be helpful to your students, or it may just further
muddy the waters - you decide!

A great deal of mathematical notation comes into being because it is   
useful
as a means of compacting into more concise and "visualizable" language   
what
would otherwise be cumbersome and less easily interpretable. This is not
just an advance in convenience; it often provokes otherwise hidden   
insights.
Thus, every (3 dimensional) vector equation is shorthand for three scalar
equations (and used to be written that way).  In much the same way, an
equation involving complex numbers is shorthand for two equations   
involving
only real numbers.

 -Bob

Bob Sciamanda   sciamanda@edinboro.edu
Dept of Physics   trebor@velocity.net
Edinboro Univ of PA  http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA   (814)838-7185

 -----Original Message-----
From: Seckinger, Jennifer <jsecking.ucs@smtp.usi.edu>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Date: Sunday, February 01, 1998 5:24 PM
Subject: IMAGINARY NUMBERS


> 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
>
> *************************************************************************  

>

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