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NNTP-Posting-Date: Sat, 18 Apr 2009 15:34:34 -0500
From: "Jon" <jon8338@peoplepc.com>
Newsgroups: alt.math,alt.math.recreational,alt.sci.math,alt.sci.nanotech,alt.sci.physics,japan.sci.math,sci.math,sci.physics
Subject: Roots to Power Series and Newton's method for Complex Numbers
Date: Sat, 18 Apr 2009 16:34:15 -0400
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Xref: news.ccsf.jp japan.sci.math:221

I.
The complex function is simplified by expressing it as a Maclaurin series or 
a Taylor's series.  But how do I find the roots?

Even if the series diverges, I want to be able to find the root to the power 
series 1000 terms into the series.  But how?

If the series converges, what values does it converge for?

This web page explores the possibilities for a solution to this problem. 
Let me know what you think.

http://mypeoplepc.com/members/jon8338/math/id12.html

II.

I have a candidate for Newton's method, but it's a complex number.  How can 
Newton's method use a complex number as an initial approximation?  How can 
Newton's method generate answers that are complex numbers?

I have looked into it.  My answer is wrong, but you may look at it at,

http://mypeoplepc.com/members/jon8338/math/id23.html


-- 
Jon G.
jon8338@peoplepc.com
http://mypeoplepc.com/members/jon8338/math/