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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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

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Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

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JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

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Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

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Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

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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