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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I hope you're enjoying every minute in France! What an opportunity.

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Wordsmitty ✍️

about 14 hours ago
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Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

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Annette in France

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WakeUpAndLive️~Happiness

a day ago
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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

a day ago
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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
In response to "Paris, I Guess"

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

a day ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

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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 24, 2023 at 9:31am

#1057967

Hunter

Hunter
an entry for "Journalistic Intentions"

[18+]

You know what's bugged me for a long time? Well, yes, okay, "lots of things." But to keep things related to the topic:

Hunting and fishing are two of our oldest occupations. They existed in our evolutionary history long before we were recognizably human, and these occupations are followed today by, for example, cats, as well as many humans, whether for survival, commerce, or recreation. Yes, I know the joke about prostitution being the oldest profession, but the point there is the exchange of goods for services, whereas hunting and fishing provide their own goods, ones you could eat. Or trade to the prostitute.

That's not what's bugged me, though. That's just the background. The annoyance is this: in English, one who hunts is called a hunter. Okay, that makes sense and follows the general rules of English. And yet, one who fishes is, traditionally, called a fisherman.

So why is that, or, alternatively, why isn't one who hunts called a hunterman? It's a deep linguistic mystery.

Now, yes, the language seems to be moving, in its slow plod toward inclusivity, toward "fisher." But that's not my point. My point is that, while both occupations can be and, apparently, were practiced by all genders, we still ended up with "hunter" for anyone who hunts, but "fisherman" for someone who fishes (and "fishwife" for someone who sells the fish, but in that case "wife" meant "woman" and not "married woman," as it used to in Middle English and earlier).

As a side note, anthropologists used to assume that in hunter-gatherer societies, it was the men who hunted and the women who gathered. This was an unfortunate projection of then-dominant gender roles upon primitive peoples, which is yet another reason evolutionary psychology is not to be trusted. Turns out, in most cases, everyone participates. Or they don't survive.

Anyway. None of this explains why "hunter" also became the name for a shade of green.

Apparently, though I don't have a reliable source for this, hunters used to wear that color (which hunters, I don't know; I assume it's ones in the US and/or UK because we're talking about English, here). But by the time "hunter" was used to describe that shade of green, hunters had already started switching to more subdued, camouflage-like colors.

As with many words, though, the definition stuck even as the thing it referred to changed. Now you're more likely to see hunters in the US wearing bright orange camouflage—I gather this works because their principal prey, deer, don't have the visual color receptors to distinguish that from green/olive camo, but it does help the hunters to be seen by other hunters, reducing the incidence of hilarious tragedy.

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