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.

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.

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.

2 Like

October 27, 2020 at 12:05am

#996853

Time to Movie On

This one's been kicking around on my list since May, and I'm just now getting to it. Still mostly relevant, unfortunately.

Why Hollywood Should Scrap All COVID-19 Movies

I've linked stuff from David Wong before. This is another of his, and as usual, it's insightful.

At the time of this writing, we're about seven weeks away from what may be the most important cinematic release of my lifetime: TENET, the Christopher Nolan movie that appears to be about handsome modern wizards who use time magic to suck bullets into their guns:

Insightful, but not always right. I saw Tenet. It was... pretty. But not very good, and I could barely see the plot around all the holes. To be fair, I was pretty drunk when I saw it, so it's entirely possible I missed something, but as a long-time consumer of science fiction, I wasn't impressed.

But we should treasure it for another reason: It may be the last big movie that ignores COVID-19 altogether.

And that's truly a scary thought. I don't really buy it, though.

It takes place in a world that has never heard of COVID-19 and I want Hollywood to know that I'm fine if every upcoming movie takes place in that same world.

On that point, I absolutely agree.

1. We Don't Need Movies (Or Even Plotlines) About The Pandemic

Maybe you saw headlines about how Michael Bay is working on a COVID-19 movie (or maybe they'll coyly call the pandemic something else, to make it even more obnoxious). This is a dire example of a creator badly misunderstanding what people want out of him.

Yep. Bay is associated with massive explosions for a reason. I go to the movies to watch massive explosions of... well... explosives, not massive explosions of contagious viruses that I already know happened in real life.

But I don't even need that powerful pandemic movie from a good director, ten years from now. I don't need it from anyone, ever.

Of course, we could, you know... just not go see it.

In fact, I'm good with every future movie just completely ignoring the fact that COVID-19 ever happened. I'm fine if the romantic comedies of 2022 feature unmasked characters having a meet-cute at the chocolate fountain at Golden Corral. Nobody is going to be pissed that they're not following CDC guidelines, for the same reason nobody wants to see James Bond stop to fumble with a condom.

Yep. If we wanted reality, we wouldn't go to movies. By the way, I will throat-punch anyone who uses the term "meet-cute" in my presence. Just be aware of this.

2. We Don't Need You To Evoke The Imagery Of The Pandemic, Either

Hey, remember how after 9/11, action directors started adding scenes that looked a whole lot like Ground Zero?

That, at least, had the advantage of being visually appealing. Not so with tent hospitals or small gatherings of masked individuals. Or large gatherings of unmasked individuals, also known as Trump worship services.

Right now, a whole bunch of filmmakers are likewise thinking of ways to incorporate COVID-19 imagery into the thing they're making, in the same way that not even in Star Trek can we escape shots of buildings collapsing into gray clouds.

Again, at least collapsing buildings look epic. Well. Unless they're happening in real life without benefit of clearing the place out first for a controlled demolition.

3. Actually, You Can Scrap Your Trump Movies, Too

You know what? Now that we're here, just apply everything I said above to the entire Trump era. I don't need a goddamned movie five years from now where Jonah Hill wins a bunch of awards for playing Steve Bannon. I don't need a star-studded HBO miniseries about Jared Kushner or Michael Flynn or James Comey or Sebastian Gorka or Tom Price or Scott Pruitt or Anthony Scaramucci or Rex Tillerson or Paul Manafort or Jeff Sessions or Michael Cohen or Eddie Gallagher or any of the other names I just got off the "Trump Scandals" Wikipedia page.

Movies have been made about Presidential administrations before. I never saw any of them. Again... just don't go see it. I wouldn't. And it wouldn't matter if the movie was trying to be fair, or sucking Trump's dick, or trying to beat him down. I've lived through the last four years inhaling the daily news cycle, and I agree, I don't need some cinematic effort to "put it all in perspective."

While we're on movies, you know what else I'm not going to see? The Avatar sequels.

Oh, I'm sure they'll be pretty. And I kind of enjoyed the first one, once I decided to let go and ignore the plot, science, acting, and dialogue. It's more the utter hubris of Cameron and the studios going, "You know what? We're just going to go ahead and make the next four right now, each with an enormous budget. People loved the first one, and they loved Titanic. Cameron is gold! What could go wrong?"

No, I want to see a boycott of those movies. Not for any silly political reasons, but just to send a message to Disney (the first movie was Fox, but I think Disney picked it up when they bought the studio): We're not putting up with this shit. Release one movie. If we like it, you'll make money, and then you can make the next one.

But, as usual, people are going to make the movies they want to make, despite what internet comedy writers have to say about them. And hopefully there will continue to be movies, and theaters, because the experience of going to the theater (especially the one I go to) just can't be replicated at home.

This year was supposed to be the year of me going to see a different movie in the theater every week or two. That held up well... until March. I started again when they reopened (at a much lower capacity) in August. I've seen movies I wouldn't normally see. I've disliked ones that got great reviews, and liked ones that people panned.

But no. I'm not going to want to see Covfefe-19 references in movies now, or ever. We get enough of that shit in real life. I go to the movies to escape from that shit. And to see explosions, car chases, and people in costumes fighting crime.

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