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 10, 2023 at 10:40am

#1057116

Chartreuse

Chartreuse
an entry for "Journalistic Intentions"

[18+]

Chartreuse is called chartreuse not because it's named after Chartreuse, but because it's named after Chartreuse.

I'll take it chronologically.

It starts with a mountain village now called Saint-Pierre-de-Chartreuse. I'm sure you know who Saint-Pierre was, though an alternate translation is something like Holy Rock, which makes a lot more sense, considering. "De" of course just means "of" As for Chartreuse itself, well, those origins are far more speculative; we know it was older than the Roman occupation of Gaul, and it may be named after a local pre-Roman tribe who, I'd venture to speculate, had no idea of the size of the world or that a variant of their name would one day be uttered all over it.

If I were writing fiction, I'd posit that the Gauls living around there had a particularly precious monolith that they'd make offerings near, hence "holy rock." But I'm not writing fiction at the moment; I'm doing a blog entry.

Anyway, at some point the village ended up giving the name to the entire mountain range, now known as the Chartreuse Mountains (massif de la Chartreuse).

Then, in the late 11th Century C.E., some monks took over a château somewhere in those mountains; as monasteries sometimes are, it was fairly remote. The mountains named the monastery and the order of monks, which Latinized the name: Carthusian.

The Carthusian order did whatever it was monks did for a few centuries, and then, a miracle: somehow they obtained a recipe for a particular medicinal spiced liqueur. While I'd be tempted to say it came from On High, as it were, the story goes that some guy gave it to them, and they supposedly spent the next hundred years making it better.

What they finally released to the world is, of course, today known as Chartreuse, a liqueur with a distinctive green color somewhat different from that of the related liqueur, absinthe. There are variants with different colors now, and that leads to some confusion: chartreuse can refer to a greenish-yellow, like the original Chartreuse, or a yellow, like one of its variants. Though apparently the latter is normally called "chartreuse yellow," so maybe it's not all confusing.

So, to reiterate: chartreuse (the color) is named after Chartreuse (the liquor), which is named after Chartreuse (the monastery), which is named after Chartreuse (the mountains), which were named after the (I'm guessing) holy rock of Chartreuse.

And with that, I could use a drink.

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