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.

1 Like

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.

3 Like

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

1 Like

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 5, 2023 at 10:21am

#1055201

The Man, The Myth, The Reality

Some things we think are real turn out to be myths. But sometimes it's the other way around. Cracked provides a few examples.

5 Apocryphal People That Were Actually Real as Hell

Hell, of course, is not real (except for the town in Michigan), but I suspect they mean that as an intensifer.

Of course, embellishments are natural, but the basis for what you might think are tall tales are often a flesh-and-blood fellow.

Those "embellishments" might be how myths and legends get started in the first place. Kind of like how that fish you caught that one time keeps getting larger and heavier every time you tell the tale, until everyone's convinced that you hooked Leviathan. Or, well, you're convinced they're convinced, anyway.

5. Johnny Appleseed

I knew this was a real guy; I only ever objected to his glorification. Though I suppose his legacy of spreading non-native species around is better than that of Charlie Kudzuseed or Frankie Freshwatercarpegg.

Johnny Appleseed is a tale that sounds patently insane. A man wandering the Wild West, tossing out apple seeds and leaving a trail of trees in his wake, sounds like a folk tale at best and a severely deranged man at worst.

Well, he was at base a missionary, so "deranged" isn't too far out there as a description.

4. John Henry

As far as American myths-based-in-fact go, this one's my all-time favorite.

Heck, John Henry versus the machine is practically writers’ struggle against advancing A.I. Well, if John Henry was a feeble, depressed man, and the steam machine made weird-looking, factually inaccurate railroads.

The thing people get most wrong about this one, though, isn't the human vs. machine thing, but the nature of his work: he didn't hammer spikes into ties (well, he may have done that, too, but that's irrelevant to the main story), but, as I understand it, he drove metal drill thingies into raw rock for placement of demolition charges. You know, to make cuts or tunnels in the Appalachians.

3. Paul Bunyan

Rarely has there been a better modern example of reality getting exaggerated into mythology.

Bunyan’s physical legend, it’s believed, comes from a French-Canadian man named Fabian Fournier. Remember, first, that in 1875, when Fournier lived, the average male height was right around five and a half feet tall. Given that knowledge, the six-foot-tall Fournier was practically Shaq with an axe. It’s thought that Fournier’s famous bulk combined with the name of another famous lumberjack, Bon Jean, which over time and error, morphed into Bunyan.

So, roughly contemporaneous with John Henry. I'm seeing a lot of Johns and (French) Jeans on this list. Where "Paul" came from is unclear, but I guess it played better with test audiences than "Fabian."

2. Davy Crockett

I didn't think there was doubt that Crockett was an actual person. Still, sometimes it's hard to separate the truth from the exaggeration.

1. Dracula

Hey, someone not from North America.

He is, however, based on a real, notably horrible man. Vlad the Impaler, born Vlad III Tepes, was a ruler of Wallachia, which is now Romania.

Pretty sure the the Dracula thing is widely known to be based on a real, if morally repugnant, individual. But how did he get all the attention, while Elizabeth Bathory,

arguably a far scarier individual, languishes in relative obscurity?

Probably a sexist thing. After all, you don't see any chicks on this list, do you? If I had time, I'd come up with some.

2 Like • Comment • View 2 comments

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