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.

3 Like

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.

2 Like

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.

1 Like

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

April 14, 2023 at 11:31am

#1048188

I Ain't Got a Thing...

Another fashion entry, courtesy of "Journalistic Intentions"

[18+]...

Swing

Wait, wait, hold up.

"Swing" has like 48 definitions, of which exactly 0 of them that I'm aware of fit the fashion theme. (But I know at least four that refer to sex.)

Time, then, to become aware.

For the first time in history, Wikipedia fails me here. There's the usual disambiguation page,

which parses out many of the 48 (I pulled that number out of my ass, but doesn't seem to be far off from reality) possible meanings of the word "swing." Not one of these refers to clothing.

So let's try that old standby, Merriam-Webster.

Nope.

Now, look, I'll save us both some time here: best I can figure out, the only clothing-related use of the word "swing" that I could find anywhere refers to a dress style from the 1950s.

I hadn't been born yet; I'm generally bewildered by nuances of fashion; I don't wear dresses; I've never been in a serious relationship with someone who regularly wore dresses. So my lack of knowledge here shouldn't be surprising (though it's at least partly fixed now). Still, it makes me wonder why both WIkipedia and one of the leading American dictionaries failed me.

Apparently, from what little I can piece together (most of the search results I found were vendors, which is even less reliable than Wikipedia, and hopefully this morning's frantic Googling will confuse the living shit out of someone at the NSA), the swing dress was for dancing to... wait for it... swing jazz.

Which I have heard of, because unlike fashion, music is an actual interest of mine. Though I'm not generally fond of jazz.

But there is one advantage of ignorance: I can use it to make shit up.

So, obviously, the first thing I thought of was that it might be the clothes that swingers wear. As that might be ambiguous, I'll note that by "swingers," I mean the partner-swapping scene. But that wouldn't make sense; as far as I know, swingers don't use clothing to differentiate themselves from monogamists.

Maybe... clothes to wear on a swing? When I was a kid and could still fit on swings, we just wore whatever we were wearing. Which led to quite a few skinned knees.

Or, ooh, I know! it's clothing that'll change your political affiliation. "Here, wear this vest. It'll make you vote for the Libertarian and like it."

Compared to even my lousy imagination, though, the reality is—as per usual—quite disappointing, at least to me. That is, of course, assuming that I'm somehow right, which is a massive assumption. It's disappointing to me because, to me, there are only three kinds of dresses: 1) Wedding dress; 2) Bridesmaid's dress (look, I used to be a wedding photographer); 3) Dress.

I don't believe in only learning shit about shit that affects me. But even I can't hold unlimited information in my noggin, which is why things like search engines and dictionaries and encyclopedias are my friends (and auxiliary memory). Even an established nerd like me needs to let some things pass unnoticed, or I'd be overwhelmed with trivia. It's annoying and frustrating to me when such references fail.

But hey, at least I learned something new today. Again.

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