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 9 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 5, 2024 at 9:04am

#1076299

Writing It Off

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive

Prompt 5. Sept 5.

The more that you read, the more things you will know. The more that you learn, the more places you'll go. Dr. Seuss
Tell us more about the writer in you. Plans/Aspirations/Fears/Status etc?

Plans: None. As a writer, anyway. Apart from continuing to do what I'm doing now. Other than writing, I plan to travel more. I may write about it, but the travel writing field is crowded with young influenzas who can't write for shit, but look good in selfies.

Aspirations: None. Used to be, I wanted to get published. I abandoned that goal, I don't know, maybe about when I turned 50? No one wants to publish old, unestablished writers. Well, almost no one. You can probably find a counterexample if you look for one, because it made the news. It made the news for the same reason lottery wins and lightning strikes do: it's rare. Plus, I'd have to be an exceptional writer. I may be a decent writer, but I'm not exceptional in any way.

And don't say "self-publishing" at me. While it's absolutely a legitimate route, it involves way more work than I'm willing to do, including marketing. I hate marketing, not to mention it would be hypocritical of me to push ads on people while hating all the ads being pushed on me.

Not that I'm above being hypocritical, of course. That just seems a step too far.

Fears: Tornadoes, picking up dog shit, anything touching my eyeballs, and success.

The tornado thing is probably understandable. Not that I live in an especially twister-prone area; it's just that they are, to me, natural disasters worse than earthquakes, floods, fires, or volcanoes.

Picking up dog shit is just something that grosses me out. Thus, I don't have a dog. Every once in a while I'll owe a favor to someone, and sometimes that favor means walking their dog while they're on vacation. Just because I can work through my fears doesn't mean I want to. (Before you ask, cat shit doesn't bother me as much, though it's still not my favorite chore to clean up.)

I also dealt with the eyeball thing a few years ago, because I had to. That doesn't mean I'm eager to have eye surgery again.

The "success" one does relate to writing. Let's say a miracle happens and I get one of my novels published. Suddenly, I'm expected to write more. You know what happens to me when I'm expected to do something? It becomes work, and I'm violently allergic to work.

Status: Another English word with more than one meaning. From context, I'm guessing this is the "how are things going" definition, as in "status report." Answer: cruising along. As for the other definition, where I fit in the social hierarchy, well, I reject the concept of a social hierarchy. But that's really irrelevant; I just like to play with words.

In any case, there is one writing-related thing that's been on my mind lately. As I've mentioned a few times, I've done a blog entry every day for nearly 5 years. Whether it's prompted like this one, or a spontaneous personal update, or commenting on some article, I've managed to find something to say every day since December 14, 2019. This wasn't planned; I just blogged every day for a few months, and the plan after that was to go to Scotland for a couple of weeks for the Islay Festival. Then, well, you know what happened in early 2020. I didn't go anywhere. I kept blogging. When I finally was able to go somewhere, I stayed in the US, and still managed to get an entry in every day.

This will end.

It may end during my upcoming Europe trip, now only 2 weeks away. That's not the plan, but it could happen. My shit gets stolen or broken, or I can't connect to the internet, or I just get too busy and/or too drunk, or I fuck up the time zone difference. I don't know.

Ideally, though, I continue on this track until at least December 13, completing a 5-year daily blogging streak. That's as close to a "plan" as I get with writing, these days.

In either case, though, blogs here are limited to 3000 entries, and this is entry number 2812. Less than 200 to go. Enough to take me to early next year if I continue at this rate, but then... bam! Brick wall.

Other people here have dealt with the limit by deleting old entries. I won't do that. Most never have to worry about the limit, and that's perfectly okay. But I've been considering what to do next. Quit? Start a new blog? Concentrate on fiction and poetry for a while? If I started a new blog, I'd have to think of a title that's somehow works as well as, or better than, Complex Numbers, and on that front, I'm stumped.

Oh well, at least it wouldn't be work.

Heading into the last days of Birthday week, now. We get to give out a free Merit Badge every day this week. Want one? Anyone who comments here before 11:30 pm WDC time today could get today's. (I'll need that extra half-hour to pick a winner and send the badge before midnight.)

To clarify:

When I say "comment," I mean comment. Not review. Though reviews are always welcome.

I also mean "here," not on the newsfeed post.

MB recipient will be chosen at random.

Maximum of one MB per commenter for the week.

If I don't get comments, I'll pick a previous commenter, and maybe not at random.

The MB will be the one I commissioned two years ago, "Complexity," which is a publicly available MB.

I appreciate all comments; this is just a little incentive.

4 Like • Comment • View 12 comments

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