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.

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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

August 29, 2023 at 9:58am

#1054797

What's Wrong Ain't Right

It's maddening. I'm over here losing my goddamned mind. Look... it doesn't matter how many times you repeat an error, it's still an error. It's still wrong. Like, it doesn't matter how many people mistakenly use "it's" as a possessive pronoun, or "your" as a contraction of "you are," those are objectively wrong and can never be right, no matter how much English changes otherwise. (This, of course, doesn't mean I never make inadvertent mistakes like that.)

Similarly, claiming that tomorrow's full moon is a Blue Moon is objectively wrong and can never be right, even if it is being propagated by formerly trusted sources of mine like Atlas Obscura. It makes me call all of their "facts" into question. No, I'm not going to link their offending article. One stupid mistake in a magazine back in the 1940s, and this is what we get: rampant, viral misinformation, combined with anchoring bias (which is the one where the first thing we hear about a certain topic sticks in mind, even in the face of arguments evidence to the contrary). Ugh.

As for the "supermoon" thing that you've probably heard in conjunction with that (that's a very obscure pun, because a full moon occurs at opposition, while a new moon represents an astronomical conjunction), well, whatever. It's a real thing, though probably overhyped. By all means, if you can gaze at the full moon tonight and/or tomorrow night, I encourage you to do so. Here, it's supposed to be cloudy. Of course.

At least I only have to do this rant every three years or so (except for the time a few years ago when we got two full moons in January, none in February, and two in March, which for fuck's sake should have ended that false definition once and for all). With luck, I'll be dead the next time the false Blue Moon comes around, and you won't have to see me kvetch about it.

For the record, once more with feeling, the actual Blue Moon is the third full moon of a season containing four full moons, and the next one occurs next August. It can never occur in the last few days of a Gregorian calendar month.

Eh. This is long enough now that I don't need to get into a random article today. One might say this happens once in a Blue Moon; that is, one can say it if one wants me to start this rant all over again. I'll get back to my usual format tomorrow. I will, however, link one of my longer arguments in favor of the traditional definition, in the form of two consecutive Fantasy newsletter editorials:

"It's Not a Blue Moon, Part I"

"It's Not a Blue Moon, Part II"

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