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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Write_Mikey_Write!

5 minutes ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

Adherennium Plotting something

about 2 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

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Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

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Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

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JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

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Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

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Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
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Not gonna lie I need the holiday season chatter.

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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