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 21 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🎁

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?

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.

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August 17, 2024 at 8:48am

#1075381

Alt-Tablet

Still no settled schedule for my voyage. It's kind of hard to plan when I don't know when I'll be leaving or returning. The agent emailed me on Wednesday to say they'd get that to me by the end of the week, but, well, here it is Saturday.

This week, I looked at computer/tablet options for the trip.

See, I'm not going to bring my expensive gaming laptop. One, I would be devastated if it got lost, stolen, or broken; two, I'd be tempted to use it for its primary function instead of, you know, looking at Europe or whatever.

I will bring my mobile phone, but if I want to write blog entries, or notes about the wines I taste, or whatever, I'll want something with a keyboard. It's gotta be able to connect to the internet in Europe, and run basic programs like Word, but it's not like it has to run Starfield or whatever. Something like a Chromebook, maybe, or similar.

So, I started looking into tablets. The kind that flip into mini-laptop mode.

I got frustrated quickly. I don't know what half the numbers mean, or how to compare them. A lot of the shit out there is cheap-ass junk. I don't really care how much it costs; I just want it to be somewhat reliable, and one cannot rely on internet reviews for that sort of thing. But some of them are surprisingly cheap, less than $200. Which, well, how do I know if I can trust that?

The idea is to get something I can use on the trip, but also be a backup computer if my main one crashes suddenly, which they've been known to do. Right now, the only backup is my mobile, and I hate typing on a screen. Not enough tactile feedback.

It might be that I have to go (shudder) outdoors and (gulp) talk to someone at a (shiver) retail store who can point me in the right direction. Or, hell, maybe the travel agent has recommendations, since I already ventured out to talk to them. As long as it doesn't take them another month to get back to me on that.

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