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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 8 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 10 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.

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.

June 13, 2022 at 12:04am

#1033771

Bar Wars

Entry #4 for June's "Journalistic Intentions"

[18+]...

Bad Guy Bar

Bars are so obvious that using them in storytelling borders on cheating.

They're usually a semi-public place (hence the name of the British version), so you get all kinds there, and the opportunity for both planned and chance meetings. This is, perhaps, no better illustrated than by the famous cantina scene (a cantina is, from what I've gathered, a bar in a desert) in Mos Eisley in the original Star Wars.

Han shot first, by the way. I have spoken.

Setting your scene in a bar, especially early on, is a kind of Chekov's Phaser

for me: If the rest of the story progresses without a bar brawl breaking out, I'm usually sorely disappointed.

I can only imagine the level of fight choreography that goes into filming a bar brawl. To make them look realistic enough, everyone has to know exactly what they're doing, while making it seem like everything is unplanned. I guess that's why they get paid the big bucks, though. You'd have to time everything just right, and be sure you know the difference between a real bottle and the fake ones used for bopping people upside the head, or the difference between the real chairs and the breakaway ones used for bopping people in the kidneys.

Gotta say, I love a good bar brawl scene, whether it's in a Bad Guy Bar or wherever. I mean, you don't usually get those kinds of fights in a library, or at Wal-Mart, though I suppose someone's probably done it in a movie just for variety's sake.

But sometimes, those scenes just don't work.

An actual melee fight is, by nature, chaotic. If you're in one, you can't keep track of what's going on; you just have to try to avoid getting hit while trying to make sure the other guys don't. Never ask me how I know this. Filming an actual bar fight, for instance from the perspective of a hypothetical security camera, you'd see a lot of flailing around, but there's no focus, and you only get one angle. This doesn't work in a movie, so there needs to be attention paid to the important parts at just the right time, as otherwise you lose the audience.

I've seen bar fight scenes where they don't do that very well, perhaps in a bid to capture the feel of an actual bar fight. Lots of quick cuts, and sometimes you can tell by where things are or what the characters are wearing that it took about seventeen takes and the result is a mashed-up edit of different parts of the footage.

And, other times, I've seen ones where someone, say, throws a punch, but the angle's all wrong, so you can tell it's a stage punch. You know, missing by a mile while the "punchee" twists their neck like they've been socked. How that gets past the editors and director, I have no idea, unless they were spending the entire scene finding the bottles of real liquor and drinking them.

Unfortunately, though, bar brawl scenes give bars a bad name. Of all the purveyors of fine distilled and fermented beverages that I've been to in my life, from sawdust biker dives in Montana up to the Ritz and every level in between, I've never once witnessed an actual fight break out in one. I'm not saying it never happens, but I've been to a lot of bars and I've never seen one. Watch movies and shows, though, and one might get the idea that walking into a bar is like you might as well be carrying a lit match near kegs of gunpowder.

But one shouldn't expect realism from movies. I can't count the number of times I've seen a scene filmed at a rave or concert, and the main characters are just standing there talking without saying "WHAT?" after every sentence the other one speaks. Loud bars are loud. I can't hear myself in them, let alone anyone else. You want to talk to me in a noisy bar? Try using a pen and paper, because my knowledge of sign language is limited to "hello," "thank you," and "up yours." Better yet, just let me enjoy my beverage in peace. I'm not there to socialize or get into fights; I'm there to drink.

And don't get me started on when a character makes a phone call in the middle of a DJ's set. That shit just doesn't work. Texting might, though.

But none of that gives bars a bad name the way fight scenes do. And yet, like I said, I love a good one.

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