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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Elisa: Middle Aged Stik

a day ago
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a day ago
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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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September 15, 2023 at 10:11am

#1055769

Going Bananas

It's a promo on LitHub for a book, but whatever. We're all readers here. And it tracks with what I already knew.

How the Banana Came To Be—And How It Could Disappear
Emily Monosson on the History, Evolution, and Biological Enemies of a Staple Fruit

Yesterday, I bought some bananas, and noticed that since the summer, they had doubled in price!

...from 12 cents each to 24.

(This is one reason you have to beware of that sort of emotional language when you encounter it.)

I still find it difficult to believe that a banana's actual worth, a couple thousand miles from where they're grown, is less than a quarter. I'm sure there are all sorts of subsidy shenanigans going on, and low-paid workers involved, but I can't be arsed to research it.

Bananas are a fruit that unites the world.

Not so sure about that, but as fruits go, they're definitely one of the easiest. Peel and eat, no messy juice, no seeds. I saw a video once where a creationist took that and ran with it as "proof" of intelligent design. Well, they were intelligently designed, all right: by intelligent humans, who genetically engineered a seed-infested fruit with very little meat and turned it into a snack as easy to eat as a Milky Way bar.

Though there are thousands of varieties, most of us in the western world eat only one: the Cavendish.

Or, as we tend to call them here in the US, "bananas."

Of the twenty-two million tons of bananas exported to the United States, Europe, and Asia, most are grown in Latin America and the Caribbean.

I still remember a brief tour of a banana plantation in Belize. But this article goes into a lot more detail around the growing and shipping process, which I'm not going to repeat here.

The banana plant is easy to mistake for a tree, but it is the largest known herbaceous flowering plant.

This is a distinction much like tomato being, botanically, a fruit.

The plants grow, produce flower and fruit, and die.

Ready-made metaphor there.

The article also goes into the rise and fall of the previous kind of shipped banana, the Gros Michel (commonly translated to English as "Big Mike," but I prefer "Fat Mikey.") That's fairly widespread knowledge now, as is the whispers, going on for some years now, of the soon to be certain demise of the Cavendish.

Hasn't happened yet, but with banana prices doubling here, maybe it's happening?

What the article doesn't get into is whether there's a suitable, fungus-resistant successor to the Cavendish. We can be pretty clever with our bioengineering and selective breeding, so I expect they'll find a way. Otherwise, based on the numbers in this article, a whole lot of people are going to find themselves unemployed.

And, worse, I'll have to find another easy fruit to like. And that, for me, holds no ap-peel.

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