Complex Numbers (Book)

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Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

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February 27, 2022 at 9:36am

#1027530

Escape to L.A.

Since I'm traveling, I'm just going to try to post some daily updates instead of the usual stuff. When I'm at home, it's rare that something happens that's worthy of blogging about for more than one or two sentences. Like maybe I'll see a movie, and then I deliberately do a one-sentence review. Of maybe my cat does something funny, but I don't want to waste space here on an image item so it's not something I can usually blog about.

Anyway, so, yesterday, I drank.

Okay, I know, big surprise.

Another big surprise was that, after the major departure delay I've already discussed, both of the flights I took left on time and arrived early. This offended my sense of reality, because I was sure that something else was going to go wrong. It had to. Maybe, I thought as I waited by the baggage claim at LAX, maybe the airline sent my checked bag to Cleveland. I mean, this would suck, of course, but at least it would vindicate my view of the universe.

But no, my bag was about the sixth one off the carousel.

Several years ago, I flew out to Vegas. Similarly, I was waiting at baggage claim, figuring either my bag had taken a left turn to Albuquerque or fell off the carrier and was broiling on the hot McCarran tarmac. But no, behold, the very first bag off the conveyor was mine. "Well," I thought. "This will never happen again."

So that's what I was thinking of when I pulled my suitcase off the baggage claim, because nothing else had gone wrong: "I was right. Mine wasn't the first bag off the belt."

Anyway, I spend the rest of the day hanging out with Annette in France

and her family. We went up to Mount Wilson Observatory, for starters, which won't mean much to you unless you're an astronomy nerd, but for us astronomy nerds, that place is a Pretty Big Deal in terms of the history of astronomy. For example, it holds the telescope that Edwin Hubble used to figure out that galaxies were galaxies and that the universe is expanding, which was one of the most massive paradigm shifts in the history of science.

When we got back to L.A., then I drank.

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