Dear Gary:
Robert is correct in what he says in his tutorial. (Well, there is an
obvious transcription error in the answer of the last example.) However, if
you use a typical calculator to perform some of the calculations, there is a
potential problem.
ArcTan(b/a) can, and eventually will, give you the wrong number. As an
example: If a = 1 and b = 1, obviously the angle is 45 degrees, and the
ArcTan function will present 45 degrees. Consider the case where a = -1 and
b = -1: most calculator's ArcTan functions will still return 45 degrees.
So, if using a typical calculator and the ArcTan function, make a sketch
to estimate what the angle should be and correct the calculator's
presentation accordingly.
The introduction of complex numbers, which were once part of "pure"
math, and the concept of impedance made (and continues to make) circuits
much more easy to deal with than was previously the case.
Enjoy, 73 Mac N8TT
--
J. Mc Laughlin; Michigan U.S.A.
Home:
"W9DMK (Robert Lay)" wrote in message
...
Dear Sir,
Try the program "Vectors" at either of the following Web sites. By
plugging a few examples into the program, you will again understand
complex arithmetic.
http://zaffora.f2o.org/W9DMK/W9dmk.html
http://www.qsl.net/w9dmk/
The program does not run under an NT based system, such as Windows XP
or Windows 2000 but it will run fine in DOS under Windows 9x or
Windows ME.
Here is the short tutorial on complex arithmetic:
a1 + jb1 + a2 + jb2 = (a1 + a2) + j(b1 + b2)
The rule for subtraction follows the obvious complement to the above
example of addition.
In order to do complex multiplication and division it is easier to
convert first to polar form, as follows:
Magnitude of a + jb is sqrt(a^2 + b^2) and the Angle is arctan(b/a)
In Polar form the product of two vectors is the product of their
magnitues and the angle on the product is the arithmetic sum of the
two angles.
In Polar form the quotient of two vectors is the quotient of their
magnitudes with an angle that is the difference between the
numerator's angle and divisor's angle.
Example: 5@35 * 6@40 = 30@75
5@35 / 6@40 = 0.8333@-40
where @ means "at an angle of"
Bob, W9DMK, Dahlgren, VA
http://www.qsl.net/w9dmk