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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Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 6 hours 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.

1 Like

🐕GeminiGem🎁

about 10 hours 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

about 12 hours ago
In response to "Trash Pandas"

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

4 Like

Jayngle Bells

about 12 hours 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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2 Like

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

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

November 14, 2024 at 11:16am

#1079935

Global Domination

Back in the early days of this blog, I had a running joke about ragging on Hello Kitty. Very recently, I found this article from Fast Company:

Hello Kitty turns 50: Here’s how she became a global moneymaker
As Hello Kitty’s commercial success expanded beyond Asia, so did her personal profile.

At least, I thought of it as a running joke. Looking back, it might have seemed like a serious hate-on. Either way, though, the whole reason for the gag was the Nefarious Neko's worldwide appeal, how the character seemed to be everywhere, on all things, in all contexts.

This, of course, is successful marketing. As I've said before, I sometimes put marketing articles in here because many people have things they want to promote, like, maybe, their books. And also, the psychology of it can be interesting.

Hello Kitty turns 50 on Friday.

For context, if you don't want to click on the link, "Friday" was November 1 of this year.

As a tabula rasa open to interpretation, the non-threatening creation was the perfect vehicle for making money, she said.

This strikes me as opposite to most marketing advice, which is to know your audience and pander to it. In the past, I'd have taken issue with the "non-threatening" description, but again, I think those jokes fell flat.

There have been anniversary editions of merchandise ranging from pet collars, cosmetics and McDonald’s Happy Meals to Crocs and a Baccarat crystal figurine.

On the other hand, I'd have had a field day with Hello Kitty Crocs. Hell, I might still be able to work up a rant about that particular combination.

By the late 1970s, Sanrio revealed the character’s name as Kitty White, her height as five apples tall and her birthplace as suburban London, where the company said she lived with her parents and twin sister Mimmy.

That much, I knew. ("Know your enemy," I might have said in the past.)

Her TV appearances required co-stars, including a pet cat named Charmmy Kitty that made its debut 20 years ago.

This was also always suspect to me. A cat owning a cat? Isn't that, like, slavery?

But Hello Kitty’s 40th birthday brought an update that astonished fans. Sanrio clarified to a Los Angeles museum curator that Kitty, despite her feline features, was a little girl.

Thus sidestepping the "slavery" issue and pushing the conversation back to animal rights. Just kidding; I doubt anyone else thought deeply about the ethics involved.

“She is supposed to be Kitty White and English. But this is part of the enigma: Who is Hello Kitty? We can’t figure it out. We don’t even know if she is a cat,” art historian Joyce S. Cheng, a University of Oregon associate professor, said. “There is an unresolved indeterminacy about her that is so amazing.”

Like if she were in a box with a radioactive atom. Schrõdinger's Hello Kitty.

Part of the confusion stems from a misunderstanding of “kawaii,” which is Japanese for “cute” but also connotes a lovable or adorable essence.

It may be cliché, but some things really do get lost in translation.

During a presentation earlier this year in Seoul, Hello Kitty designer Yamaguchi said one of her unfulfilled goals was finding a way “to develop a Hello Kitty for men to fall in love with as well.” But she’s still working on it.

I have some ideas, but I try to keep this blog 18+.

Even if I'd been serious about my ragging on Hello Kitty, that came to an end some years ago, when I read an article (which I can't find now) featuring some village in Northern Siberia, considered the most remote human settlement in the world (pretty sure they didn't include Antarctic research bases, just places where humans naturally settled). Of course, the village isn't entirely unreachable, or they wouldn't have done an article on it, but apparently, it's only accessible by some rickety train line in the week when there's summer there.

The article included pictures, and in one of them, a little girl in this remote village unconnected to the world at large was wearing a Hello Kitty shirt. That is when I knew that her dominance was complete, and no amount of rage, joking or otherwise, would end her hegemony.

Honestly, these days, I think we could do a lot worse.

5 Like • Comment • View 2 comments

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