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

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Elisa: Middle Aged Stik

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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 6, 2023 at 8:45am

#1056859

Plum

Plum
an entry for "Journalistic Intentions"

[18+]

Ever prune a plum tree?

One of the many linguistic confusions that plagued me as a kid—alongside such old standbys as flammable/inflammable and the various pronunciations of -ough—was a result of us possessing a plum tree.

We had lots of fruit and nut trees. A miniature almond orchard adorned our front lawn; the garden was peppered with walnuts. Off to the side stood several fruit trees, including apple, peach, cherry, and plum.

All of those fruits are somehow used to connote something good or desirable. For instance, my father claimed I was the apple of his eye, at least until I did something bad (which was, of course, a regular occurrence, at which point he would pare me, and not spare the rod). When things are going well, people say they're "peachy" (but they also say that when everything's going to the pits, because people love sarcasm). A really nice thing can be "cherry," and, of course, a particularly great job is a plum assignment.

You know what's not a plum assignment? Picking fruit and nuts off of trees. My dad was too old to be climbing trees, and there were a couple of years in there between "too young to climb trees" and "too teen to care about anything."

But all of these trees, and others, needed to be pruned on a regular basis, and that's what caused me the greatest confusion.

Because a dried plum is called a prune.

Now, I heard it through the grapevine (we had one of those, too) that those words, plum and prune, are linguistically equivalent, unlike, say, grape and raisin. And there's no special word for dried cherries; they're just dried cherries. The botanical binomial for the various species of plum trees starts with prunus, which is obviously where we get prune (dried plum), but not prune (the verb), which, through a tidal wave of linguistic gymnastics, also traces its origin back to Latin... but this time, from the word "rotundus," which, if you've been paying attention, obviously means "round." I guess it came from the practice of making trees look round, like a kid would draw? I don't know. Contrary to popular belief (which I foster), I don't know everything.

None of which explains how we got "prune" from "rotundus." The more recent etymological ancestor, according to the online dictionary I just looked at, is an Old French word: prooiginier, which I guess I can see.

All of which is to say it has nothing to do with plumb, plumber, or plumbed, which comes from the Latin word for lead. The metal.

If this is confusing, well, good. Welcome to my world.

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