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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Brandiwyn🎶

a day ago
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
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

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October 22, 2022 at 12:03am

#1039534

Smackdowns

Every art form eventually gets to the point where artists are doing it for fellow practitioners of the art rather than for mass consumption. Writing passed that point ages ago, sometime between Shakespeare and Melville, but fortunately, there's still writing for the masses.

14 Classic Works of Literature Hated By Famous Authors
"I got a little bored after a time. I mean, the road seemed to be awfully long."

And yet, an argument could be made that no one is more qualified to critique a book than someone who's written a book. But that never stopped me, and it never stopped the millions of people who never made a movie from critiquing a movie.

The literary world can be a bit of an echo chamber. That is, if enough people say a book is “great,” it becomes official. It becomes a Great Book, and horrified looks are administered to anyone who would dare disparage it.

Yeah, I do it anyway. I'm looking at you, Ulysses. Yes, that book is on this list; just wait for it.

But even when everyone seems to agree, it’s a safe bet there are a few—or in some cases more than a few—dissenters out there. They may just be in hiding.

I'll have to trot out (again) one of the greatest literary smackdowns, if not the greatest, of all time. At the end of this post.

Virginia Woolf on Ulysses

I started to rub my hands together in gleeful anticipation until I remembered I'm not a big fan of Woolf, either.

An illiterate, underbred book, it seems to me; the book of a self-taught working man, and we all know how distressing they are, how egotistic, insistent, raw, striking, and ultimately nauseating.

How I can agree so much with her conclusions while still gaping in disbelief at her elitist snobbery is beyond my comprehension.

A first rate writer, I mean, respects writing too much to be tricky; startling; doing stunts. I’m reminded all the time of some callow board school boy, full of wits and powers, but so self-conscious and egotistical that he loses his head, becomes extravagant, mannered, uproarious, ill at ease, makes kindly people feel sorry for him and stern ones merely annoyed; and one hopes he’ll grow out of it; but as Joyce is 40 this scarcely seems likely. . . I feel that myriads of tiny bullets pepper one and spatter one; but one does not get one deadly wound straight int he face—as from Tolstoy, for instance; but it is entirely absurd to compare him with Tolstoy.

True. Tolstoy could actually write.

Dorothy Parker on Winnie-the-Pooh

But wait! You might say. How can anyone go all Eeyore on Winnie-the-Pooh? The original, I mean, not the Disney version.

“ ‘Well, you’ll see, Piglet, when you listen. Because this is how it begins. The more it snows, tiddely-pom—’

“ ‘Tiddely what?’ said Piglet.” (He took, as you might say, the very words out of your correspondent’s mouth.)

“ ‘Pom,’ said Pooh. ‘I put that in to make it more hummy.’ ”

And it is that word “hummy,” my darlings, that marks the first place in “The House at Pooh Corner” at which Tonstant Weader Fwowed up.

And it was at this point that I actually Laughed Out Loud.

Charlotte Brontë on Pride and Prejudice

Wasn't that the prequel to Dumb and Dumber?

Why do you like Miss Austen so very much? I am puzzled on that point.

Me too, Charlotte. Me too.

I mean, really, I can't do this takedown justice here. You just have to go to the link. It's beautifully understated.

Mark Twain on Pride and Prejudice

Also the author of what I'm calling the greatest literary smackdown of all time... again, later.

I haven’t any right to criticize books, and I don’t do it except when I hate them. I often want to criticize Jane Austen, but her books madden me so that I can’t conceal my frenzy from the reader; and therefore I have to stop every time I begin. Every time I read Pride and Prejudice I want to dig her up and beat her over the skull with her own shin-bone.

This. This is why Mark Twain is one of the greatest writers who ever lived.

Skipping a few here in the interest of time.

David Foster Wallace on American Psycho

Unlike most of the others, this is still a kind of contemporary book. At least it was published in my lifetime.

Look, if the contemporary condition is hopelessly shitty, insipid, materialistic, emotionally retarded, sadomasochistic, and stupid, then I (or any writer) can get away with slapping together stories with characters who are stupid, vapid, emotionally retarded, which is easy, because these sorts of characters require no development. With descriptions that are simply lists of brand-name consumer products. Where stupid people say insipid stuff to each other. If what’s always distinguished bad writing—flat characters, a narrative world that’s cliched and not recognizably human, etc.–is also a description of today’s world, then bad writing becomes an ingenious mimesis of a bad world. If readers simply believe the world is stupid and shallow and mean, then Ellis can write a mean shallow stupid novel that becomes a mordant deadpan commentary on the badness of everything. Look man, we’d probably most of us agree that these are dark times, and stupid ones, but do we need fiction that does nothing but dramatize how dark and stupid everything is?

Burrrn.

And the list ends as it begins: with a flamethrower pointed straight at James Joyce.

Vladimir Nabokov on Finnegans Wake

I detest Punningans Wake in which a cancerous growth of fancy word-tissue hardly redeems the dreadful joviality of the folklore and the easy, too easy, allegory.

But alas—it turns out that Nabokov actually liked Ulysses. Oh well. No one's perfect.

And now, as promised, although I'm sure I've linked this here before, it makes me laugh every single time I read it: the greatest literary takedown of all time... Mark Twain on Fenimore Cooper.

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