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!

a day 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.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

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

3 Like

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.

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.

September 9, 2019 at 12:12am

#965855

A Happy Medium

PROMPT September 9th

Prompt today is straight outta the War Chest courtesy of Robert Waltz

!

What is your favorite storytelling medium, and why? Face-to-face? Movies? Novels? Audiobooks, audioplays? Stage productions? Comics? TV shows? Tweetstorms? Concept albums? Something else?

Well. I guess I have no excuse to skip this one, do I?

Full disclosure: I remember posting that prompt in an "add to the War Chest" round of a previous 30DBC. You'd think after 12 years or so of being a judge at "Invalid Item"

, I'd be better at creating prompts, but I'm not. When I come up with a really good one, I keep it to myself, because then I want to use it. I only post the ones I wouldn't care to respond to, myself. So that came back and bit me on the ass. Fortunately, this one was the result of a promptstorming session I had with PuppyTales

, so it's not... entirely mine. Okay, it's mostly hers. Okay, it's like 98% hers. I think I added "tweetstorms" to be funny, because that's what I do.

My answer is different depending on whether I'm writing or reading. Obviously, I'm a big fan of books; I mean, why else would I be here? I started reading at an early age, and never stopped. Books, or at least printed-word stories, are what I write. Both writing and reading them exercise the imagination.

But when it comes to consuming media, probably my favorite story type is the TV show.

That wasn't always the case. For a long time, I didn't watch TV at all. I mean that as in, I didn't even own a TV. It wasn't until streaming became a thing that I got back into that particular medium. Sturgeon's Law applies, as always: 90% of it is utter crap. But now, being able to watch shows without being interrupted by commercials (which I hate with the nuclear fire of a thousand suns), I see the artistry in it.

There was a massive shift in TV writing that occurred about the time I stopped watching. One of the last things I saw on TV before I gave it up was Babylon 5 (and I didn't finish it at the time). It introduced what would become a mainstay of 21st century TV writing: the story arc. I think Straczynski stole the idea from comic books - that while each episode can be self-contained, there would be an overarching plot that stretched through an entire season (that's series for you Brits), ideally resolved at the end. This was done with varying levels of success, of course.

That simply wasn't the case when I was younger. A single show might refer to an older one, sure; or there might be a "To Be Continued" multi-episode story; and shows like Doctor Who (back then) were serialized in 4-6 episode chunks, but the idea of a season-long story arc was pretty much unheard of before the early 90s. I should note that a single season of Doctor Who, back in the seventies, experimented with this, but it didn't catch on until much later. And the "arc" elements in that one stayed mostly in the background. (If you're wondering I'm referring to The Key To Time, Fourth Doctor, Season 16.)

What you end up with is a televised novel with a series of chapters, or something very like it. Opinions may vary, of course, but that method of storytelling holds my interest better than a bunch of disconnected episodes, even those with a common theme.

Meanwhile, you have time for character development, time that's lacking in such things as movies or short stories. You can do it in comics, too, of course, and I used to be a big-time comics fan also. As I said, the story arc concept was basically invented for comics and only later migrated to TV.

So, in short - writing: traditional short stories and novels, because I lack the skills to do more than just write. Consuming: episodic television, because of the opportunity to tell much longer stories and present intriguing character development.

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