🚀 go-pugleaf

Martin Dick wrote:
> 
> Hello. I am in need of an explanation of the theory of complex numbers and
> their uses. I have consulted several textbooks tending to this subject but
> they are all far too advanced for my case.
> 
> I also need an explanation of how complex numbers relate to fractal images
> as fractals are a useful aid in artificial intelligence decision making.
> This sort of research can allow computers to make decisions of their own by
> relating fractal`s infinite complexity to the organised tree like formation
> of computer databases. This enables _logical_ decision making and
> re-inforces artificial common sense.
> 
> Uses of this type of system could include helping the disabled by letting
> the computer perform operations with less strenuous user input and the idea
> of computers making decisions in dangerous situations where humans are too
> slow to think (nuclear power plants, hospitals, etc,) - this could save a
> lot of lives. Thanks.
> 
> --
> E-mail:
> torbain@globalnet.co.uk
   Start with a good book in electronics covering AC theory.

                     imaginary
                         ^
                         |   /
                         |  /
                         | /
                         |/  angle
-------------------------+--------------------> real
                         |
                         |
                         |
                         |
  First, think of simple cartesian coordinates where a point can be
expressed in terms of distance in X and Y.  An alternate way of
describing the same place is in polar coordinates; angle and distance
from reference.
  Now think of AC power to a component, and use the voltage as a
reference (reference phase or zero phase).  Then let that component be a
capacitor and measure the current thru it; it will be out of phase in
relation to the voltage.  Since a capacitor opposes a change in voltage,
the current will "lead" or be ahead of the voltage in phase by 90
degrees (for a perfect capacitor, and most are quite close to this).
  So now you see the angle part; the distance is related to the amount
of current.
  In electronics, this relationship is expressed as a complex number for
calculation purposes, hence the reference.
  The above is like a drop of water; get the book or books and get wet!