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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Write_Mikey_Write!

about 6 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

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Adherennium Plotting something

about 8 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

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Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

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.

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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.

May 24, 2021 at 12:17am

#1010635

On with the Show

PROMPT May 24th

Write about a movie or television show you watched recently that blew you away. What lessons can you learn from the show and incorporate into your own writing?

Hm. Well. I might be too cynical these days to really get "blown away" by movies or TV. I go in to all of them from the point of view of a writer: What works? What doesn't? Why does what works, work? Even bad movies or shows can teach me something, but my time is as limited as anyone's, so I don't often deliberately seek out bad ones. Still, if I happen to come across one, I approach it from a writer's point of view so as to learn what doesn't work.

I've mentioned before, in here and in a recent Fantasy newsletter editorial, that I enjoyed Godzilla vs. Kong. While I can't say I was in any way transported by it, the movie was very enjoyable. But what can you learn from it as a writer, besides "have giant monsters fight each other while wrecking an entire city?" Well, I covered another aspect in the newsletter; if you haven't seen it, you can view the editorial here: "Giant Monsters"

Besides, city-destroying kaiju battles don't usually translate well to fiction writing. Their impact is solidly visual.

My TV show consumption nowadays consists of two main interests: comic book shows, and Star Trek. The latter is mostly new stuff; it's rare that I want to revisit them, because there are so many that I just don't have the time. With Trek, again as I've noted in here before, I'm on a quest to (re)watch every episode (and movie) in that franchise, in chronological order. As I write this, I just wrapped up Season 4 of DS9 and Season 2 of Voyager, both of which I mostly missed when they first came out in the mid-90s.

A lot of Trek is objectively silly. But it's popular for good reasons, and I've been trying to, as I mentioned above, figure out what works and what doesn't. To me, it comes down to a few basic ingredients.

Characters. Say what you will about Trek, but they have memorable characters. Everyone is aware of Spock, for instance. Or Worf. There's a huge advantage in having characters like them in stories, because they can provide contrast to the absurdity of some human behaviors and customs, by virtue of being outsiders. It's a trick as old as science fiction itself, and it works. But even setting aside the alien characters, the humans in Star Trek generally have well-defined personalities, inner conflicts, likes and dislikes, strengths and flaws.

Plot. Unless you're setting up a cliffhanger at the end of a season or something, wrap things up. In life, things rarely resolve themselves in 45 minutes, but we don't watch SF shows for the realism. It's very satisfying to a viewer (or reader) to provide a firm conclusion to whatever conflict has gone on in the episode, be it a plague that only the ship's doctor can cure, an alien attack on a colony that needs to be resolved by a starship captain, or a malfunctioning transporter that requires engineering expertise. Or whatever. Wrap it up. Sometimes Trek shows don't do this very well, and it sticks out when that happens.

Subplot. Often there's more than one plot involved, because we can only take so much tech gobbledygook before someone does a miracle and fixes everything, so maybe you have a different character bemoaning her love life, or dealing with a personal crisis. This is fine, and it keeps the actors who may be unnecessary for the main plot busy in accordance with their contracts. But from a viewer's perspective, it can be used to create suspense as the subplot unfolds at critical moments in the main plot, or vice versa. But for Kahless' sake, give the plots some parallelism, if only on a metaphorical level, or we start losing patience with the whole thing.

Humor. Okay, maybe I'm biased about this because I consider myself a comedy writer (whether other people consider me a comedy writer is something the jury's still out on). But inserting a bit of comedy into an otherwise tense situation is a very effective technique for keeping the audience engaged. It's basic writing: any emotion can only be sustained for a limited amount of time. That's why they call it "comic relief;" you get relief from the relentless problems the cast are dealing with. The trick is in finding the appropriate level of comedy for the situation. If a bunch of characters are dying all around you, you don't necessarily want a Vaudeville act unless you're going for farce in the first place. But a well-placed one-liner here and there can make the difference between a good plot and a great one, while also illuminating character. And then, once in a while, you get a whole show about tribbles.

Above all, though, what I learned from Star Trek is: don't put space hippies in your show. That was cringeworthy enough in the late 60s, and today, it just comes across as silly.

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