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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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