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!

about 8 hours 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.

1 Like

Adherennium Plotting something

about 10 hours ago
In response to "Global Domination"

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

3 Like

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.

3 Like

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.

2 Like

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.

1 Like

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.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

January 5, 2024 at 8:48am

#1061923

Shrug It Off

I do like a good literary takedown... though only when I agree with the person doing the takedowning. This one's from LitHub.

Read a 1957 review of Ayn Rand’s “excruciatingly awful” Atlas Shrugged.

The article is from last October 10, which is important to note because it starts out:

Today is the sixty-sixth publication anniversary of Ayn Rand’s 1100-page magnum opus of unreadable doggerel libertarian science fiction, Atlas Shrugged.

Using strikethrough style is, of course, a cheap trick, one where the writer is coyly covering their mouths, giggling, and going "Oops, did I say that out loud?" And it makes me laugh almost every time. Yes, even when I do it. Especially when I do it. In this case, though, the article author did it; I just reproduced it here.

Still, calling AS "unreadable," even in strikethrough, is a bit unfair. It is, by some definition of the phrase, readable, in that it contains words, and those words are (as I recall) spelled correctly and ordered according to English grammatical practice into sentences and paragraphs.

Set in a dystopian United States in which private businesses suffer under increasingly burdensome laws and regulations (isn’t it always the way), it’s the story of railroad executive Dagny Taggart and her lover, steel magnate Hank Rearden, and their struggle against the “looters” who want to exploit their productivity.

Hence the "fiction" part. Here in reality, it is the "captains of industry" who loot the labor of the workers and exploit their productivity.

Despite receiving largely negative reviews upon its release, the novel sold briskly and became a formative text for numerous conservative/libertarian ghouls politicians and thinkers...

That's the trouble with science fiction, good or bad: there's always someone out there trying to make it happen. Sometimes, that's a good thing. Sometimes, it's not.

One prominent conservative critic of Rand and her philosophy was William F. Buckley Jr., whose National Review published this scathing review of the novel by (Communist spy turned HUAC whistleblower turned book critic) Whittaker Chambers in December of ’57.

So, the rest of the article is Chambers' original review, from which I'll quote only sparingly.

It is the more persuasive, in some quarters, because the author deals wholly in the blackest blacks and the whitest whites.

People being unable to handle nuance is hardly a new thing.

So the Children of Light win handily by declaring a general strike of brains, of which they have a monopoly, letting the world go, literally, to smash. In the end, they troop out of their Rocky Mountain hideaway to repossess the ruins.

Here in reality, those who we today lump into "billionaires" wouldn't last a week in the Gulch, not without the near-slave labor that cooks for and cleans up after them.

It is then, in the book’s last line, that a character...

Look, I don't care how terrible the book is, or how spot-on the review otherwise is; spoiling the last line is cheating.

But the words keep shouting us down. In the end that tone dominates. But it should be its own antidote, warning us that anything it shouts is best taken with the usual reservations with which we might sip a patent medicine. Some may like the flavor. In any case, the brew is probably without lasting ill effects.

And here the review falls apart, for here we are, two-thirds of a century later, and some people still treat that book like it was handed down from Mt. Sinai.

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