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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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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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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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
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WakeUpAndLive️~Happiness

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

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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 24, 2023 at 10:20am

#1056151

Revisited: "What's Good for the Propaganda"

Today, we're going only about 4 years into the past for this entry from August of 2019: "What's Good for the Propaganda"

The entry was, as mine have mostly come to be, prompted by an article. And the article, from Fast Company, is still up for now. It's a quick read if you're interested; it's about design as propaganda.

I don't have much to say about my own comments, so I'll get them out of the way:

That last tide seems to be turning, now, thanks to Elon Musk making electric cars that people might actually not be embarrassed to be seen in, as opposed to the pug-ugly "Smart Car."

Boy, this bit didn't age well, did it? Though I stand by my assertion that Tesla's cars are aesthetically pleasing (and, reportedly, usually functional), Musk went ahead and crashed and burned like one of his other companies' rockets. As a result, today, I'd be embarrassed to be seen in a Tesla, regardless of how cool it might look. It's a disgrace to its namesake now.

I don't usually think about it, which makes me a sucker. But I'm going to work on it.

And I think I have, though I'd forgotten this particular article and entry over time.

What I didn't do in that entry is take a look at the article itself, so I'll do a bit of that now. So the following quotes are from the article, not my entry:

By elevating everyday, inexpensive objects that fit the museum’s criteria of “good design,” MoMA paved the way for modernism to hit the mainstream, launching the careers of seminal designers like Eero Saarinen and Charles Eames and displaying designs that visitors could actually buy.

There's a problem with the word "modern," and I think I've touched upon it before. It can be used as a noun or adjective to describe something that's roughly contemporary, as opposed to obsolete or outdated. That definition is a bit slippery, as some cultural or technological things change faster than others.

The other meaning of "modern" describes a particular artistic or aesthetic movement, one which probably peaked around 1950 or so (but I'm not an expert on these things). Whatever the actual end date was, what's called "modern" in art is now obsolete, thus rendering it not "modern" by the other definition.

Oh, and in case you're not aware and don't want to read the article, "MoMA" refers to New York's Museum of Modern Art, which, despite me being a critic of just about everything inside it, is a great place to visit in the city. Or at least it used to be; I haven't been there for several years.

There was a secondary motivation for the Good Design institution as well: economic expansion, both at home and abroad. According to Kinchin, the Good Design exhibitions, which were established in conjunction with the Chicago Merchandise Mart, played a key role in educating the American consumer about why they should be buying these kinds of American household products.

So, the whole thing was basically an ad.

In other words, the Good Design exhibitions were marketing. Stores that wanted to sell objects that had been featured could emblazon them with the program’s logo, a red dot with the words “Good Design” written inside. Catalogues for the exhibitions also included exactly where people could buy each product, like a glorified showroom with an institutional stamp of approval from the MoMA curators.

Yep. Ad.

The competitions, which were accessible to all, also opened the door for European designers to find a foothold in the U.S. market. For instance, MoMA’s 1950 International Competition for Low-Cost Furniture Design was meant to generate new furniture that could be mass-produced.

Clearly, this resulted in the hegemony of Ikea, which I also mentioned in that earlier entry, accompanied by the words "stay the hell away from."

That's about it for me. There's obviously more in the article.

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