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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QPdoll

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WakeUpAndLive️~Happiness

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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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WakeUpAndLive️~Happiness

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Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

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Elisa: Middle Aged Stik

a day ago
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https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

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WakeUpAndLive️~Happiness

a day ago
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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 13, 2023 at 7:44am

#1057294

Amethyst

Amethyst
an entry for "Journalistic Intentions"

[18+]

Way back in the murky mists of deep time, during a period when I was on the fence about being childfree or not, I knew what I wanted to name a daughter: Amethyst. That would even be my red flag, I decided. When I'm dating someone, I find out if she likes the idea of naming a girl Amethyst and, if not, we weren't going to go any further.

This lasted, oh, about a month or so, when I dated a woman who hated the idea, but was really smoking hot, so all of those plans went right out the window. It wasn't long after that, probably, that I decided my actual red flag was "I want kids."

But I digress; the point is, I liked the sound of that word for as long as I can remember. Which is actually a fairly long time, as I was told early on that it's my "birth stone," just because I arrived in February.

"Birth stone" is, of course, a transparent marketing gimmick, like those silly lists of anniversary gifts. Regardless, I liked the sound of the word amethyst, and I liked the deep purple tint of the stone.

It's just quartz, you know. Silicon dioxide, the second most common mineral of the Earth's crust. (The first is feldspar, which really shouldn't count, as it isn't always composed of the same elements the way SiO₂ is.)

Of course, amethyst isn't really "just" quartz. That color comes from the occasional iron atom in the crystal lattice. Don't ask me why that makes it purple, though; it probably involves quantum effects.

So yeah, common or not, I have a thing for amethyst. Or, at least, I did, until I found out the etymology of the word. It's probably common knowledge by now, but I'll reiterate it here anyway: the word comes to us from ancient Greece, though they certainly weren't the first people to know about the mineral. They assigned it the mystic property of protecting a person against drunkenness, so they named it not-intoxicated, or, in their words, a-methyst.

From what I understand, they even made goblets of carved amethyst on the theory that you could drink all you wanted to out of them and not get drunk. If they'd been half the scientists people think they were, though (and I have an article in the queue that touches on the ancient Greek penchant for natural philosophy), they might have done controlled, double-blind tests and realized that no, it possesses no such property, and any perceived resistance to the blessings of Dionysus was essentially a placebo effect.

I don't know how this belief didn't piss off Dionysus. And you don't want to piss off Dionysus; he's a mean drunk. I, however, am not a mean drunk; I'm a lot meaner when I'm sober. So even though didn't possess this magical quality, the mythology made it lose some of its sparkliness for me.

Therefore, it's just as well I never had kids to saddle one with a name I'd grow to distrust.

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