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

January 11, 2021 at 12:00am

#1001857

Pleasantly Surprised

PROMPT January 11th

Write about a recent movie, documentary, or TV show you watched that you did not expect to enjoy, but actually did. Give your readers some recommendations!

Here's the thing, though: I really can't do that.

That is, as much of a pessimist as I am, these days, I only get into shows / movies that I expect to enjoy. Since I'm single and there's a pandemic going on, I'm not subjected to people pestering me to watch something I wouldn't otherwise. On the occasions when that's happened, back when I still had friends, it usually lives down to my low expectations. Now, there have been countless times when the opposite occurred: when I expected to like a piece of entertainment, but ended up disappointed. The last Star Wars movie, for instance.

Around the same time that came out, however, there was a movie I expected to utterly detest, but ended up liking. It was over a year ago, though, so it doesn't count as "recent." This was a movie that pretty much everyone in the universe, and beyond, hated... except for me. To hear the internet talk about it, you'd think it was a massive black hole of suck and was responsible for earthquakes, tidal waves, tornadoes, and the pandemic. (I'm sure the fact that it came out about when the pandemic started was purely a coincidence. Well, mostly sure, anyway. Pretty sure.) I fully expected to hate it, based on the trailers and early reviews; I mostly just went to see it as a joke, but it turned out to be a really enjoyable movie.

I'm talking about Cats.

Look, I eschewed bandwagoning years and years ago. I'm not going to pretend to dislike something just because the internet says it sucks; conversely, I'm not going to pretend to like something just because it's popular.

And I'm not saying the movie was a masterpiece or anything, but it was way more enjoyable than I expected.

You know, after The Empire Strikes Back came out, lo these many years ago, I was in my teens. And I remember hearing from someone at my school that they planned to make it a trilogy, and then do a prequel trilogy, followed by an ending trilogy. I also remember thinking, back then, "Damn, I gotta stay alive to see the end of this trilogy of trilogies, because Star Wars is fucking awesome."

And I know I posted this here before, on my newsfeed, right after Cats and The Rise of Skywalker came out, but again -- it's been over a year. So I'll paraphrase it here as best as I can remember it:

I went to see TRoS and Cats on the same weekend. Afterward, I hopped into my time machine to have a chat with Kid Me, shortly after he saw Empire.

"Greetings! I am Future You."

"Oh yeah? What's with the beard?"

"Shut up. I'm here to reassure you that you will, indeed, live long enough to see the end of the Skywalker saga."

"Awesome!"

"That same weekend, you will see the film version of an Andrew Lloyd Webber musical."

"Eww! Grody to the max! Gag me with a spoon!"

"Sigh. Stupid eighties. Anyway... you're going to hate the Star Wars movie and love the musical."

"...what? Bullshit."

"Would I lie to you?"

"NOOOOOOOOOOO! No, it can't be!"

"Search your feelings. You know it to be true."

Point is, if I couldn't convince Kid Me of this, there's no way I could convince anyone else.

Still. I'd totally see Cats again.

11 Like • Comment • View 13 comments

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