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 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.

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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.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

June 6, 2022 at 12:04am

#1033417

Utopia

Entry #2 for "Journalistic Intentions"

[18+]...

Crapsaccharine World

We've been conditioned.

Thanks to fairy tales, comics, books, shows, movies, etc., most of us take certain ideas as absolute fact. These include:

If it seems too good to be true, it is.

When wishes come true there's always a heavy price.

Utopia is impossible.

A lot of this is because, were it not so, the story wouldn't be very interesting. "One day, little Angela found an old lamp and rubbed it. A genie came out and granted her a wish. She wished for a pony. She got a pony. They became fast friends and lived happily ever after."

That's not a story. That's an anecdote you tell in an actual story, one with conflict and characterization and plot and shit like that.

You could say that the biggest part of a fiction writer's job is to think about everything that could go wrong, implement some of it, and have the characters deal with it. Preferably they actually succeed in the end, but that's optional. So, faced with a utopia (a concept that, at its very inception, was meant as satire), we're programmed as writers to search for flaws, any flaws.

An early episode of ST:TNG comes to mind. In it, they find a utopian planet where everyone is young, fit, blond, and mostly naked, wearing the bare minimum to get past 80s TV censors (I will just say, as an aside, that William Ware Theiss

, the costume designer for TOS and TNG, was a goddamn genius). Everyone on the Enterprise is pumped to be there, especially that absolute dog Riker. And then Wesley (of course) fucks up and discovers its horrible secret first-hand. This leads to Picard bending the Prime Directive to the breaking point, and it's in the running for my award of Worst TNG Episode, despite the preponderance of ultra-hot Nordic babes.

Trek itself, from the get-go, was conceived as a utopia of sorts: a post-scarcity technoparadise where everyone (mostly) got along. Later shows subverted this, mostly after Roddenberry died. Else the property wouldn't have lasted as long as it did: 55 years and counting.

A real utopia, if it's even possible, would simply be too boring to write about.

Which is one reason I've never accepted the idea of Heaven. Leaving aside for the moment the metaphysical issues, the concept of spending eternity in a golden cloud city surrounded by angels playing harps sounds more like Hell to me. I mean, Hell itself doesn't sound too great, but damn , those (and every other) concepts of an afterlife make utter nonexistence seem pleasant by comparison.

The only way to make Heaven work is to alter peoples' minds so that they believe it works, at which point, if you can simply make people happy by manipulating emotion and perception, there's no need to actually create a utopia. It'd be like that meme where the dog is sitting there surrounded by fire going: This is fine.

As long as your mind is in thrall and you never wake up to reality, you'll stay in utopia. Yes, yes, I know, The Matrix did something like that. I maintain that the movie, for all its excellent special effects, was entirely derivative.

The whole thing reminds me of the famous Milton quote: "The mind is its own place, and in itself can make a heaven of hell, a hell of heaven." Which I'm still convinced he cribbed from Shakespeare.

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