🚀 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!

We help people with problems here, not people who want a college degree.

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



--
Jim Berwick
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Its quite simple really.

A complex number is of the form x + jy where j is the squareroot of minus
1.

Don't let j put you off because you will never have to work out what it is.
All you have to do is square it.

So j squared is minus 1.

It now becomes easy to multiply two complex numbers together as follows -

(a + jb)*(c + jd)  =  ac - bd + j(bc + ad) which is just another complex
number.

Think of j as a radioactive tracer which allows the "imaginary" components
to be kept track of in the course of a long calculation.

And thats all there is to it - well almost. But it's all very easy.
-- 
Reg  G4FGQ
http://www.btinternet.com/~g4fgq.regp

In article <01bd9f1d$19766760$8c2e63c3@default>,
  "Reg Edwards" <g4fgq.regp@btinternet.com> wrote:
>
> Its quite simple really.
>
> A complex number is of the form x + jy where j is the squareroot of minus
> 1.
>
> Don't let j put you off because you will never have to work out what it is.
> All you have to do is square it.
>
> So j squared is minus 1.
>
> It now becomes easy to multiply two complex numbers together as follows -
>
> (a + jb)*(c + jd)  =  ac - bd + j(bc + ad) which is just another complex
> number.
>
> Think of j as a radioactive tracer which allows the "imaginary" components
> to be kept track of in the course of a long calculation.
>
> And thats all there is to it - well almost. But it's all very easy.

I don't know about it all being very easy, but here's the other standard
results you need: (a + jb)+(c + jd)  = (a+c)+j(b+d) (a + jb)/(c + jd) 
=(a+jb)*(c-jd)/(cc+dd)

mod(a+jb)=sqrt(aa+bb)
theta(a+jb)=atan(b/a)  ....(but get the right quadrant)

a+jb=mod(a+jb)*exp(j.theta)

Their great advantage is that in exponential form (the last equation) you can
manipulate 2 dimensional numbers in one expression.

On a graph, you plot the real part on the x axis and the imaginary part on
the y axis.





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j can also be considered as an operator on a vector.

Multiplication by j rotates by 90 degrees.

Multiplying twice by j rotates by 180 degrees  -  ie, in the opposite
direction and hence the change in sign.  ( j squared  =  -1)