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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June 4, 2022 at 1:01pm

#1033351

Beer. That's Why.

Back from the beer festival. Instead of my usual, I thought I'd talk about *gasp* my experience.

So, a little background that I'm not sure I've shared here before: I got the beer fest tickets months ago, when they first went on sale. The theme of the festival was queer beer; that is, not beer that is weird, but breweries that are run by lgbtqia* (or whatever the latest label is) folks.

Now, you may be wondering why I, the most heterosexual man in the universe, would be doing at a queer beer festival. Well, first of all, I've long been an ally, as I'm a proponent of individual freedom. Call it performative virtue if you need to be cynical about it, but I don't think I would be much of an ally if I didn't publicly support these marginalized groups.

The second and more important reason, of course, is beer. Beer doesn't have a gender or sexual orientation. It's just beer. I don't care what the brewer identifies as; I just want to try the beer. A beer festival is a great way to sample brews from all over. And this is the first one I've had a chance to attend since the Before Time.

It might occur to someone to wonder "where's the straight beer festival," to which I'd respond that probably over 90% of breweries are run by straight bearded white dudes, so sometimes to highlight diversity you need to put it out front. Believe me, there are plenty of other beer festivals where the majority can do their thing, too. Or will be; not so much the past couple of years.

Anyway. I was supposed to go with my housemate, but she broke her leg, which of course sucks and tends to keep one from traveling comfortably for a while. As the tickets were nonrefundable, I went with a different friend (after making sure someone else could be here for the housemate).

I do have to say, I was moderately disappointed by the festival itself. A couple of rows of tents on a pier poking the Potomac, with the main sponsor's tent (New Belgium out of Colorado) taking up one end like a throne. Most beer festivals, I get overwhelmed by the choices; here, there just weren't that many. Maybe a couple of dozen. But like I said, minorities are minorities, especially in the beer community, so it shouldn't be surprising that there were relatively few vendors. At least that meant I got to try something from pretty much every booth.

By "try," for those unfamiliar with beer festivals, I mean "sample." Different jurisdictions have different rules; for example, here in Virginia you get four-ounce samples. Apparently in DC it's only two ounces, which is certainly enough to get a taste of the product. So no, it's not like I went from tent to tent having a pint at each. Not even I could have done that. I'd have ended up floating down the river. With no regrets.

After a couple of hours of this, of course we had dinner and went to pass out. Which is how I expected it to go, and why I did warn you today's entry would be delayed.

I expect tomorrow I'll go back to the regularly scheduled program.

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