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.

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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.

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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.

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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.

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.

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November 29, 2021 at 12:02am

#1022488

Future Perfect

If you don't have regrets, you're doing it wrong.

PROMPT November 29^th

Imagine for a moment that you are near the end of your life. What do you want to have done that would make you feel satisfied?

What do you mean, "imagine?"

Everyone has some regrets, I think. Not necessarily the mind-consuming ones like "Oh, I shouldn't have jumped off that cliff, plunging me into a lifetime of pain," but little things, like "I really should have asked her out," or "Damn, I should have had the lasagna instead."

Nothing wrong with having regrets; I just think it's counterproductive to dwell on them for too long.

Like, one thing I wish I'd done when I could was see the Roger Waters version of Pink Floyd in concert (or any Pink Floyd, really). Or Led Zeppelin. Both of those eras ended when I was in high school, though, so it's not like I had a whole lot of agency in the matter. But I don't live my life thinking every day about how awesome that would have been. Besides, I have seen other performers that I like, and I'd rather remember those than the might-have-beens.

But with the use of the future perfect in the prompt, I think the intent is: what do I want to do between now and my inevitable embarrassing demise that would make me feel satisfied before I kick it?

Well, other than having a romantic interlude with Halle Berry, which ain't gonna happen; or maybe finding the Fountain of Youth, which is marginally more likely... really, not much. Some traveling, if things would fucking settle down. I've done much of what I'd set out to do, and I'm fine with what few regrets I have. (Occasionally you'll see me making references to having lived my life toiling in the regrettium mines of Regrettistan, but that's for humorous effect and not to be taken seriously.)

So, no, I'm good. I'm pretty damn satisfied. Smug, even. Yes, I'm insufferable (you think that's bad, try having beers with me). It's not like there aren't things I still want to do, but that would be the case even if I lived until the heat death of the Universe.

And no, I have no reason to believe I'm actually near the end of my life. But I have no reason not to believe it, either.

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