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 8 hours 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

a day ago
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🎁

a day ago
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

a day ago
In response to "Trash Pandas"

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

4 Like

Jayngle Bells

a day ago
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?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

September 24, 2024 at 9:03am

#1077221

All Out of Louvre

So, yeah, I didn't go to the Louvre yesterday.

Look. I'm not a young man of 55 anymore. Sometimes, my knee hurts. Yesterday was one of those times, because I'd spent the last two days hiking around Paris.

Paris was never the purpose of my trip. I agreed to three days there because I figured I could use the time to get over any jet lag, and see firsthand how bad my French pronunciation is [Narrator: vraiment très mauvais], and also to meet my new friend there. No, the purpose of the trip was wine tasting in the countryside, and beer drinking in Belgium later.

If I'd gone to the Louvre, that would have been more walking and standing and stopping and staring. I would have liked to have seen some of the art, of course. But not the Mona Lisa. There's only one reason to see the Mona Lisa, and that's to be able to brag that you've seen it, while complaining about how small it is and how crowded with tourists the room is. The obvious hypocrisy there is that you're contributing to said crowds.

I can skip the seeing it bit and accept the information that the painting is surprisingly small and the room is extremely crowded.

Besides, if I can't paint a mustache on it, what's the point?

So, in an effort to preserve my walking ability for the really important stuff (chateaux and wineries and such), I kept things pretty low-key yesterday while my knee recovered. But I did get a bit of walking in. For instance:

Remember how I said most French beer is ass, except for some breweries in the east? One of those breweries produces a lager called 1664. It's a fairly large brewery that exports, so we get bottles back home. I've heard it's pretty popular in England, too. I buy it to drink when I want a lager, because it's a better alternative for that style than the pisswater the big names try to pass off as lager. Anyway, I found it on tap at a restaurant near the hotel, so of course I ordered one, and it was even more delicious than the bottled and exported version.

And also, if I'd wasted the day at the Louvre, I never would have encountered this delightful example of street art:

7 Like • Comment • View 4 comments

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