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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January 1, 2021 at 11:59am

#1001205

Happy New Beer!

PROMPT January 1st

What’s something GOOD that happened in 2020?

I have a confession to make:

2020 wasn't a terrible year for me.

Oh, sure, I was visited by the Fifth Horseman of the Apocalypse. His name is Minor Inconvenience. Death, Pestilence, War, and Famine don't talk about him much.

I'm not trying to downplay how horrible the year was for a lot of people. I'm not as self-centered as I sometimes project myself to be. Hence why I call this a "confession." I know it was a really rough year for a lot of folks, and I still don't see it getting any better just because a clock struck midnight. Ideally, I should go on being empathetic toward the plight of others, but right now, with this prompt, I'm just going to take a moment to gloat about how I, personally, was largely untouched by the tides of 2020. I didn't get sick; no one I'm close to died; and life continued to be, as I noted in yesterday's entry, unfair in my favor.

Sure, there were things I wanted to do that I couldn't, such as travel, theater movies, and drinking at bars. As I said: minor inconvenience. And there were a few moments of deep despair, but they were mostly fixed with music and alcohol, the combination of which often cures what ails me.

There is, of course, no guarantee that this will continue. As I also noted in yesterday's entry, luck can be fickle, and fortunes can reverse at any time. But as far as the big bad wolf of 2020 goes, he didn't manage to huff and puff and blow my house down.

One good thing about 2020?

I survived it, and even prospered in spite of it.

I appreciated all of the comments from yesterday. Some of them made me feel really good indeed. I'm so glad that people get something from what I write in here, sometimes. Another confession: here it is, 12 hours into the new year, and I find myself still drunk from last night. So I don't trust myself to pick Merit Badge recipients at random right at the moment. Perhaps after some more Advil and a nice nap, I'll be able to roll the virtual dice. Bad enough I have to judge and prompt at "Invalid Item"

as soon as I'm done posting this.

One thing I'll continue into 2021: mini-contests. So everyone will have another chance soon.

Another thing I'll continue: Zoomies. Our next meeting is tomorrow, and I'm pretty sure I'll be sober for the start of that. Probably not the end of it, though. If you haven't chimed in, maybe it's something you'd like to do this year, just to hang out and chat about writing and life in general. You can find more information here:

WDC Zoomies (Closed March 2022)

(GC)
A group of writers who meet via Zoom every 1st and 3rd Saturday
#2220189 by Charity Marie - <3

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