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 6, 2024 at 9:23am

#1073610

Down in the Valley

Might as well continue to discuss my travel plans on Saturdays. For now.

Nothing really changed this week. I'm supposed to meet with the travel agent on Wednesday, at which point I'll hopefully have a better idea of what I'll be doing.

The shifting political climate in France is a bit concerning, but it's hard to imagine it making them any more grumpy about American visitors. And I say "visitor" because that's how I prefer to think of myself, though, in this case, it'll be hard to make a case for that over "tourist."

If the situation does deteriorate, though, I might just concentrate on Belgium. Plenty of stuff I want to see (and drink) there.

From everything I've heard, the grumpiness is mostly a Paris thing, and it's not my plan to spend much, if any, time in that city. Though I'll schedule the visit to begin after the Olympics, I'm sure Parisians will have had their fill of tourists going in Seine.

(No. I will not get tired of that pun anytime soon.)

So let me tell you one thing I know I want to do (whether I'll actually get to do it or not is a different issue): spend some time in la Vallée de la Loire,

a region in western and central France.

The Loire valley may not be as well-known as Burgundy or Bordeaux, but it's a huge wine-making area. Other agriculture is prominent, too, from what I hear, but I don't care much about that bit. Specifically, I'm interested in Vouvray, which is a white wine (chenin blanc) that benefits greatly from the particular soil and climate of the valley. They export a few bottles to the US, and it's generally delicious; what I want to do is try the ones they selfishly keep to themselves.

Chenin blanc produced elsewhere is usually ass, but Vouvray is my favorite white wine.

There are also les chàteaux, which are usually interesting, historically and architecturally. Seeing castles is a remarkably touristy activity, but whatever. I did some of that in England and Wales, although the French castles are reportedly much better preserved.

I want to do other stuff, too, but a trip to the Loire valley has been on my fuck-it list for many years.

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