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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last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

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Elisa: Middle Aged Stik

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Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

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WakeUpAndLive️~Happiness

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WakeUpAndLive️~Happiness

a day ago
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Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

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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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