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
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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.

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February 16, 2021 at 12:02am

#1004582

Battlefield Earth

Entry #4 of 8 for "Journalistic Intentions"

[18+]

Battlefield Earth

You're all expecting me to rag on Hubbard here, aren't you? Aren't you? But no, the organization he founded has armies of lawyers and this shit is public.

Instead, I'm going to take this opportunity to talk about science fiction.

I talk about it sometimes in my Fantasy newsletter editorials, because there's a lot that fantasy has in common with science fiction. Incidentally, I really hate calling it "sci-fi," but I have been known to abbreviate it as SF. Rarely, though, because that could also mean "speculative fiction," which is probably a broader concept but I can't be arsed to get into the technical nuances of the differences between genres. I'm certain that for some people, it's their hill to die on.

But, as much as SF has in common with fantasy, there are important differences. I mean, yes, I'm intimately familiar with Clarke's Third Law ("Any sufficiently advanced technology is indistinguishable from magic.") I'm also familiar with the people who think they're oh-so-clever and turn it around to "Any sufficiently advanced magic is indistinguishable from technology." That's not nearly as clever as you think it is.

And I'm not saying that there aren't shades between the two genres. Hell, some of my favorite stories are somewhere on the spectrum between the two extremes. And by "extremes" here, I mean that on the one pole, you have magic and maybe the supernatural. The Platonic ideal of this is, of course, Tolkien. On the other pole you have pure science and technology, no supernatural elements, everything is explainable in terms of laws of the universe. I can't be arsed to come up with a Platonic ideal for that.

I do know it's not Battlefield Earth.

And no, it's not Star Trek, either. I love Trek, but it takes too many liberties with the laws of physics to be pure science fiction. Just to be clear, I have no problem with that; it's just a mental categorization thing.

I can also tell you that the difference between fantasy and SF isn't about time period. There's fantasy set in the future, SF set in the past, and all kinds of variations thereof. There's also fantasy set so far in the future that the basis for the magic is actually science, in accordance with Clarke's Third Law.

Before I stopped reading Orson Scott Card's books, I attended a book signing he did. As a published writer of both fantasy and science fiction, he's probably more qualified to discuss the differences than I am, a mere reader and unpublished writer. And he said: "Look at the book covers. Fantasy has trees. Science fiction has rivets."

This was before steampunk, though. Lots of rivets. No grounding in science.

Also, to be perfectly clear, Star Wars is fantasy. Sure, yes, I know, spaceships, warp drive, robots, whatever. All the tropes and trappings of science fiction. But it's not science fiction; it's fantasy that uses SF props. That is a hill that I will die on.

Again, it doesn't matter. I don't feel the need to choose, any more than I need to choose between Wars and Trek, between Marvel and DC. But genre has one important function: marketing. Some people prefer one over the other, but almost everyone wants to know, at least vaguely, what they're getting into when they start a book or movie or whatever. If it bills itself as horror, it probably shouldn't focus on romance. If it's supposed to be a detective novel, maybe don't turn it into a gothic vampire story (or if you do, at least warn us).

Other people might disagree. And that's where the battle comes in.

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