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 15 hours ago
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

about 18 hours ago
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

about 21 hours ago
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

a day 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

Dec 24, 2024 at 5:16pm
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

May 25, 2024 at 10:31am

#1071672

Banned Camp

Fair warning: this article, from Mental Floss, never really answers the headline's question. I'm still posting it, because it's may be of interest to the readers and writers here.

What Was the First Banned Book in History?
Book bans are hardly a new practice.

For a country claiming to abide by freedom of speech, we sure do love our book bans and censorship. I suppose it's just human nature: it's not enough to get your own ideas out there; sometimes, you also have to suppress those of others.

Obviously, the US isn't the only place to ban books, but in our case, it's the hypocrisy that leaves me shaking my head.

There’s no more potent evidence of the power of the written word than the fact people have historically looked to ban them.

In my opinion, if your ideas can't hold up to scrutiny and argument, then they're not great ideas to begin with. Also see: blasphemy laws.

Cultural norms, politics, personal beliefs, school policy, and other factors can all conspire to deem a book too incendiary to circulate in America.

This article is from October, so I don't remember which specific book-banning event spurred its writing. There have been so many. As for school policies, though, there's a difference between outright censorship and desiring age-appropriate materials. Some "censorship" arguments actually boil down to differences of opinion over what's age-appropriate and what isn't. Obviously, we make those distinctions right here in this community.

I've seen (and participated in) plenty of discussions about age-appropriateness, in the context of content ratings here. There are legitimate differences of opinion there. So when I talk about book bans, it's usually about people who try to keep grown adults from making their own decisions about what to read or not.

But just how far back does this policy of thinly-veiled thought control go?

If I had to guess, I'd postulate that book-banning is as old as books. Some Sumerian probably cuneiformed a dirty joke into clay, and other Sumerians got offended and tried to burn the clay, which obviously would have had the opposite of the intended effect, leaving the joke literally etched in stone.

Shattering works much better on clay tablets.

As is often the case when you look back into history, there’s more than one possible answer. But one of the leading contenders has a fairly predictable culprit: the Puritans.

Ah, yes, that marginalized group who fled religious persecution in England so they could practice it themselves in America.

In 1637, a man named Thomas Morton published a book titled New English Canaan.

So, potentially the first banned book in the Americas, but that could hardly be the first banned book, period. Incidentally, I did a whole blog entry on that author a few years ago: "Vile, Virile Vices"

His book was perceived as an all-out attack on Puritan morality, so they banned it—and effectively banned Morton, too.

The real miracle here is that their descendants ended up signing on to the whole "freedom of speech and religion" thing when they grew up.

You can go further back to find more startling examples of banned books, though the definition would have to expand to include the execution of authors.

Yeah, writing may be a fairly safe activity now, free of the occupational hazards of, say, firefighting, but it hasn't always been the case.

In 35 CE, Roman emperor Caligula—certainly a man of strong moral stuff if ever there was one—discouraged people from reading Homer’s The Odyssey because it could give them a taste of what it meant to be free.

A lot of the stuff you've heard about Caligula might have been political bickering. It would be like if the only surviving history of Kennedy's presidency was written by Nixon. And the infamous movie with his name on it wasn't exactly a documentary.

Most telling, though, there's a huge difference between being "discouraged" from reading something, and having that something banned or burned.

What book bans and censors attempt to do in the curtailing of reading is often futile.

Here is, in my view anyway, the most insidious thing about censorship: the censor has either read the book, or has not read the book. (Reading enough of the book to know you don't like it counts as reading it, in this argument.) In the latter case, it's ridiculous to ban something you haven't even read. In the former, you're setting yourself up as an arbiter, someone more qualified to make that decision than, say, me. That's also ridiculous.

If your ideas are sound, they'll withstand argument. If not, and you try to do an end-run around public discourse by banning opposing viewpoints, well, that might just make you a tyrant. And at least here in the US, whenever someone bans a book, well... that's publicity for the book, isn't it?

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