[ExI] imaginary numbers: RE: new entry from symphony of science

[spike]

2010/11/24 Darren Greer <darren.greer3 at gmail.com>

. I'm having trouble understanding how the square root of negative one could
have a practical application beyond abstract mathematics. Or even in
abstract mathematics, for that matter. ... Any takers? Remember. Key words:
FIRST YEAR. An engineer might be good here. Spike?

 

 

Darren, really are a skerjillion real world applications for imaginary
numbers.  It is actually very unfortunate that they were ever given that
name.  Calling them real and imaginary makes it sound like the imaginary
numbers are somehow not *real*.  {8^D 

 

A number with both a real and an imaginary part is called a complex number.
That is another *terrible* term, because it scares non-mathematics types.

 

They should have been called something different.  I would propose the reals
be called horizontal numbers and imaginary called vertical numbers.  Then if
it has both, it is an off-axis number, because it is on neither the
horizontal or vertical axis.

 

Here's a mathematical comment that will blow your mind if you think about it
hard enough, and one which also has real world applications:

 

  

e^(i*pi) = -1

 

I would put a ! after that comment but for the fact that ! has its own
meaning in mathematics, which makes it difficult to express one's enthusiasm
at a really exciting equation without messing up the equation.  But this is
a very exciting equation!  It is a result of the fact that

 

e^(i*theta) = cosine(theta) + i*sin(theta)

 

!!

 

Is this cool or what?

 

spike



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