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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

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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, 2024 at 10:16am

#1078731

Stark and Dormy

And now, one of my rare posts about actual writing...

2024 Bulwer-Lytton Fiction Contest

It is a truth universally acknowledged that of all the bad opening lines of literature, with the possible exception of the one that begins, "It is a truth universally acknowledged," the one that begins, "It was a dark and stormy night" is the nadir of all possible opening lines. This was from Bulwer-Lytton's novel Paul Clifford, about which literally no one outside of academia knows anything apart from the opening line.

Like all truths universally acknowledged, it's not necessarily true. But it still provides the impetus for writers to try to do worse, generally to hilarious effect.

I've posted about this before, I know, but today's entry is about this year's "winners."

Now, you'll have to go to the site to see the Grand Prize Winner. Suffice it to say that I don't agree. It's bad, but not dark-and-stormy-night bad.

I'll do what that site doesn't, which is to first paste the inspiration for the contest, the actual opening line of Paul Clifford (they put it way down the page):

It was a dark and stormy night; the rain fell in torrents—except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness.

Now, some of my personal favorites:

It was a dark and stormy night, which makes perfect sense when you realize we’re on Neptune, with a mean distance from the Sun of 4.5 billion kilometers (or 30 astronomical units), and winds that howl at 100 meters per second, composed of mostly hydrogen and helium (and only trace amounts of methane), which is way better than Uranus, which stinks to high heaven.
—Jon A. Bell, Porto, Portugal

Yes, I'd probably have selected that one as the Grand Prize Loser, mostly because I'm sick and tired of seventh-planet puns, but also because of the completely unnecessary science data.

And, of course, I'm quite fond of the Vile Puns section:

"I do enjoy turning a prophet," said Torquemada, as he roasted the heretic seer on a spit.
—A. R. Templeton, Stratford, Canada

And:

"My laddies may not be the fastest sugar cane harvesters," Fergus confessed, "but they're not as slow as my lasses..."
—Mark Meiches, Dallas, TX

Just one more; like I said, the page is there to view the other stinkers at your leisure:

Ralf Smalborgson kept a small shop in Direperil, Minnesota, and his goods consisted only of medieval stringed instruments, lanyards and backstays, and some limited apothecary supplies, giving the store its uninviting signage: Lute, Rope, and Pillage.
—Ciarán McGonagle, Derry, Northern Ireland

Which reminds me of my D&D-adjacent bard, one of whose catchphrases is, "Come on, baby, fight my lyre!"

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