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Q&A #4927

Teachers' Lounge Discussion: Pre-calculus

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2002050405:56:26
Subject: Re: jobs on imaginary numbers

On 2002011600:23:55, janine zesk wrote:
>	i would like to know what jobs use imaginary numbers in their work
>and what formulas do they use to do their job?
>

Electrical engineers and physicists in particular use imaginary
numbers.  Complete understanding of motors and generators require the
knowledge of imaginary numbers.  Even the sine and cosine functions
can be expressed in a complex form and this often permits solving
problems in Calculus that is awkward and more difficult when you don't
use them.  

Off the topic a bit, but all numbers are a subset of the complex
numbers.  

For example, when you count, instead of saying 1,2,3,4,5, etc.
You would be correct to say: 1+0i, 2+0i, 3+0i, etc., where 0i means 0
times i.

Of course the latter would be cumbersome and that is a good reason not
to do it that way.  Nevertheless, it us useful to know that is the
case.  

When you have a simple parabola which could be shaped like the cross
section of a flashlight reflector, the real roots (or zeros) are where
the curve crosses the x-axis.  When the parabola has imaginary roots,
the curve doesn't cross the x-axis and has imaginary roots.  A theorem
says that if you have 1 imaginary root, then there is at least two
because imaginary roots only occur with their conjugate.  

I will stop before this gets more boring than it is. 


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