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.

1 Like

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.

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.

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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.

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.

January 31, 2022 at 12:03am

#1025713

Controversial?

With the end of the month comes the last prompt from "JAFBG"

[XGC].

What's your unpopular writing or book opinion that you know is a bit controversial?

I've discussed some of these in here before. Honestly, though, most of my opinions are about movies, not books. It's still writing.

Some book opinions:

Ulysses is overrated. It's the literary equivalent of a Jackson Pollock painting: random noise upon which the reader can project their own patterns. No, I never read the whole thing. One should not have to read an entire book to know one doesn't like it.

This is more general, but present-tense narratives suck. They're fine for flash fiction, and practically indispensable for joke-telling ("A priest, a rabbi and an imam walk into a bar..."), but with anything longer than a short story, it's exhausting. Like reading a 70,000 word headline. (Yes, I've written stories in the present tense. Short stories.)

The first Harry Potter book was poorly written. It's been a long time since I read it, but what sticks out in my mind are way, way, way too many adverbs, clumsy scene changes, and some truly cringeworthy moments. To Rowling's credit, she got better at writing as she went along. In that case, though, I did read the whole thing. No, I'm not going to weigh in on her personal opinions; I'm only talking about the actual writing in the actual books.

Television:

"Reality" shows suck, full stop. They're not a guilty pleasure for me. Or any kind of pleasure. They are the worst kind of manipulation. And they're scripted, so their entire existence is a lie from the get-go. I'm not against lying (that's what fiction is), but don't pretend it's real. (See also: Blair Witch Project, which wasn't TV so doesn't belong in this section.)

Deep Space Nine was the best Trek. Also, Enterprise was better than Voyager (though Janeway was awesome).

Movies:

I don't get the hate for Cats. It's like everyone has to jump on the hate bandwagon once it reaches some sort of critical mass. Was it a great movie? No. But it doesn't deserve the opprobrium heaped upon it, either.

I liked the Abrams Star Trek movies. All of them. I guess that's not all that controversial an opinion, but since I mentioned Trek up there, I figured I'd say something about the reboots.

Another more general thing, but the Academy Awards are nonsense and have been for a long time. I guess the clue is right there in the name: it represents what other people in the industry think of particular movies. Which is fine. But that doesn't mean that an "Academy-Award-Winning" or "Oscar-nominated" flick is going to appeal to the uncultured masses (in which I include myself), so I don't get why people keep trying to make that a Thing. So what you end up with is people writing, directing, producing and acting in movies tailored to try to win Oscars, instead of telling a compelling story like a movie is supposed to do.

Yes, those are my opinions (though I know the prompt only asked for one; consider the others a bonus). And no, I don't expect people to agree with me; otherwise, it wouldn't be "controversial."

Speaking of movies, you might note that I haven't done any movie reviews lately. That's because the only theater I care to go to right now is the Alamo near my house, and for the last three weeks, they've had nothing I wanted to walk in the freezing cold to go see. It doesn't look good for this week, either. Naturally, this happens right after I subscribe to their effectively unlimited (one free movie a day) pass. Hopefully they'll get some soon that might be worth it to me to check out.

As for next month, I've got some articles to share, but I'll also be doing some prompts for "Journalistic Intentions"

[18+]. I'd recommend checking it out if you feel like blogging a bit next month (eight entries over the course of the month). It's not like there's much else to do in February, after all.

And finally, thanks to the folks at "JAFBG"

[XGC] for giving me stuff to rant about and for putting up with my daily posting over there.

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