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 21, 2021 at 12:02am

#1002538

Not Holding My Breath

PROMPT January 21st

What’s one thing you wanted to do in 2020 that you couldn’t do or didn’t get to do? Will you make it happen in 2021?

Well, I've covered this ad nauseam in here already, so regular readers can probably skip this entry.

The answer is "visit Belgium." I mean, there were a lot of things I didn't get to do this year that I wanted to: Nerd Camp, road trips, gambling in Vegas, meeting various WDCers in their hometowns, brewery visits, going to the gym (after February), my usual December trip to California... but the Belgium thing was something I haven't done before and was really looking forward to, and the prompt is like "one thing." So that's the one thing.

Every silver lining has a cloud... wait. Strike that. Reverse it. The one good thing about postponing my trip is that I've been able to learn more French, so by the time I do get to go -- hopefully this year -- I'll at least be able to read some of that language and maybe understand a couple of spoken sentences here and there.

Belgium, however, is a bilingual country, and I'm finding Dutch to be a much more difficult language to learn. "But it's a lot like English!" Yes, it is; it's just enough like English to be goddamn hard for me.

So it's unlikely I'll be able to pick up that language significantly before my trip. I know a lot of Belgians speak English, but I don't want to be one of those Americans who doesn't even try.

Hopefully I'll also get a chance to visit neighboring France and Netherlands while I'm there.

Will I make it happen in 2021? It's possible. What's keeping me from doing it is stuff that's totally not in my control, and you know exactly what I'm talking about. The only thing I can maybe control is getting the vaccine when it's available to me. Which I will do, but I have no idea when that will be. My traveling companion will have to get it too, of course, and then I think there's a wait while immunity builds up. And that doesn't guarantee that they'll let idiot Americans into the EU for leisure travel.

As a dyed-in-the-wool pessimist, though, I can only assume that by the time we get the shots, a mutant strain will pop up that's resistant to it and we'll get delayed again.

And even though I fully expect this to happen, if it does, I shall be quite cross.

8 Like • Comment • View 12 comments

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