[clug-progsig] 41%

Michael Walters waltersm at telusplanet.net
Mon Feb 21 21:54:05 PST 2005

Hello Shawn Grover and others on the list,

I am now about 41% the way through the absolute beginner's guide to c, and the 
last four chapters went very quickly as I saw the ways that I did certain  
things in Fortran and Assembler are easily done in c, such as incrementing 
and decrementing registers, with the added feature of post incrementing 
versus pre incrementing and post decrementing versus pre decrementing 

The things that were done in the text brought back memories of my computer 
course at SAIT between 1970 and 1976 with two years off in the middle to pay 
off the student loan, and the extra two years I took repeating failed courses 
due to relapses of my schizophrenia.

My previous knowledge from my computer courses enabled me to absorb some of 
the concepts a little faster than someone who had never graduated from a two 
year computer program.

At the rate I am now going I should complete the "absolute beginner's guide to 
c" in about 10 more days.

Then I have the other 13 c books and three c++ books to study.

In the not too distant future I expect to be able to write a c program to 
solve exp(x +jy) = x + jy where j = square root of -1.

Even if C does not have complex number functions, I could still do the complex 
number calculations using the rules of complex multiplication, division, 
addition, subtraction, and exponentiation using real number operations.

For example, exp(x + jy) = exp(x)*cos(y) + j*exp(x)*sin(y).
And (x1 + jy1)*(x2 + jy2) = (x1*x2 - y1*y2) + j*(x1*y2 + x2*y1)

et cetera.

All solutions of exp(x + jy) = x + jy come in complex conjugate pairs, a thing 
which I discovered myself, but which someone who had taken advanced analysis 
says is true of all analytic functions f(x + jy). That is the solutions to 
any equation of the form f(x + jy) = x + jy occur in complex conjugate pairs 
if f is analytic.

I was able to find three complex conjugate pairs of solutions to exp(x + jy) = 
x + jy, but I misplaced the solutions and the programmable calculators on 
which I did them are worn out. Unfortunately I have not replaced those 

However, when I learn the transcendental functions sin(x), cos(x), tan(x), 
exp(x) in c, I should be able to solve those equations and perhaps find more 
complex conjugate pairs of solutions.

I was able to prove that there are infinitely many solutions to exp(x + jy) = 
x +jy, but of course, with round off errors we can only find a find a finite 
number of those solutions.

Anyone who has successfully passed first year calculus can prove that exp(x) = 
x has no solution in the real number field. But there are infinitely many 
complex conjugate pairs of solutions in the complex field.

I expect to be able to start solving those equations using numerical methods 
and c in perhaps a couple of months.


Michael Walters - clug two tier member and member of the programming special 
interest group.

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