Talk:Complex logarithm

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[edit] History

I don't have a reference in front of me, but at some point it would be nice to include a History section in this article describing the original debate over logarithms of negative numbers. Before Euler figured it out, some intelligent men made some amusing mistakes, like forgetting about integration constants. Melchoir 21:33, 30 July 2006 (UTC)

[edit] Cut and paste

I dug back through the history on this page, and discovered that somebody named TAB did a cut and paste job from the natural logarithm page to get this thing started. Here's the permanent link if you're interested.

Anyway, I guess that accounts for the rather abrupt introduction as the article stands right now. I'm aiming to regularize the language a little bit, and maybe split it up into sections, so it will look more like a regular Wikipedia article and less like a cut-and-paste job from another article. DavidCBryant 20:39, 16 January 2007 (UTC)

I've thought about it a little more, and have formed a game plan.

• Explain the principal branch as the analytic continuation of ln(z) into the complex plane.
• Explain the principal branch in terms of the exponential function.
• Explain the multi-valued logarithm, and tie it in with the corkscrew Riemann surface.
• Clean up the expressions for log(z) in terms of x + iy.
• Add a history section, if I can get that figured out well enough. I like Melchoir's suggestion.
• Add references and links as needed.

I'm probably talking to myself here, but this outline may eventually prove useful to somebody else. DavidCBryant 21:14, 16 January 2007 (UTC)

The first cut of this article is now completed. Thanks are due CMummert for his eagle eye, and for the lovely image of the "corkscrew" Riemann surface. After some reflection, I decided to omit the conversion formulae from Cartesian co-ordinates, since these are covered adequately in many articles.

I now intend to add one more section, the complex logarithm as a conformal mapping. I think this will round out the article nicely (except for the history section, which would also be nice – facts are needed to do a good job on that). DavidCBryant 13:46, 22 January 2007 (UTC)