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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10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 11 hours ago
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

tj-Merry Mischief Maker

Dec 23, 2024 at 4:55pm
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

Dec 23, 2024 at 12:56pm
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

Dec 20, 2024 at 6:06pm
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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Annette

Dec 20, 2024 at 12:58pm
In response to "To Err Is Human"

Can I leave this comment?

July 9, 2024 at 10:52am

#1073711

Seoul Blues

Another entry for this round of "Journalistic Intentions"

[18+], in which I demonstrate that I've got no

Seoul

While I like to travel (apart from the whole "airplane" bullshit), there are some places in the world that I would actively avoid. Kabul, for example. Mount Everest. East St. Louis.

There also exist locations I definitely want to go to (which is distinct from "will definitely visit.") Places like Tokyo or Budapest, e.g.

Seoul, South Korea is smack in the middle of these extremes.

I'm sure the city has its charms. The pictures I've seen look pretty enough. There's nothing that would make me say, "yeah, not going there." I simply have other priorities.

Now, if someone were to go, "Yo, Waltz, wanna visit Seoul with me?" I'd probably say yes. Assuming I liked the person, of course. But if I only get one chance to visit that general area of the world, it'd be to sample the whiskey, sake, and delicious cuisine on the other side of the Sea of Japan.

I mean, sure, there's the whole "awfully close to their northern enemy" thing. But that wouldn't stop me. Everywhere has its risks, including sitting on one's ass at home.

Despite having been mostly destroyed during Japanese occupation (or attempted Japanese occupation; I've always been a little unclear on that particular war), the city and surrounding area apparently has lots of really cool historical tourist traps: palaces, temples, and the like. But the primary reason I travel is to experience culture, by which I mean yeast culture. And there's nothing that stands out in Korea in terms of food or drink.

Right now some of you are going, "You're nuts. Korean food is delicious." You're right; it is (or at least what makes it over here is). Except kimchi. Fuck kimchi. But so are a lot of other national cuisines.

Apparently, one of the big tourist draws of Seoul is the shopping. I'm not interested in yucking other peoples' yum, but I have near-zero interest in that activity. You know who else supposedly has great shopping? France. You know what I haven't mentioned once in my banging on about planning to visit France? Shopping.

That leaves art and architecture, and I'd definitely check some of that out if someone dragged me there.

None of this is meant to rag on Seoul in particular or South Korea in general. They're cool. I just have no more desire to visit there than I do Omaha. And at least I can drive to Omaha.

2 Like • Comment • View 1 comment

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