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.

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.

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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.

2 Like

October 27, 2024 at 9:02am

#1079008

Revisited: "Stylish"

Almost four years ago, I wrote this entry in response to a 30DBC prompt: "Stylish"

The prompt was fairly long for a prompt, so the entry was fairly long for an entry. Prompt: "What is your blogging style? In your response, consider the following questions: What is your process of writing a blog entry - do you plan it out in advance, or just start writing? Who is your ideal reader? How did your unique blogging style emerge? Has your blog changed over time?"

Upon re-reading the entry, I was a bit disappointed that few of the answers would change between then and now. There's something to be said for consistency, but there's also something to be said for growth.

Yesterday, I made my habitual Monday foray to the local taphouse.

That's one thing that's changed. I still like that taphouse, but I don't go regularly anymore.

I sit outside, on their patio, because it's a better bet than dining indoors. There are no guarantees, of course, but the science points to a lower risk of Trump Mumps transmission if you're not inside.

This has changed, of course, because it's not 2020 anymore. As far as I know, I still haven't gotten Trump Mumps... but I've had a few bouts of cold-type illness, and never did bother getting tested.

None of which really has anything to do with the prompt, except to illustrate that I don't really plan out these entries, other than maybe giving them an hour or so of thought, usually while doing something else (in this case watching YouTube videos about science, philosophy, and the philosophy of science), and then, in the entry, I could write about almost anything.

My YouTube consumption has diminished since then, also. I despise ads, and they want to charge too much for no-ads. And even without ads, I got really weary of everyone telling me to "like and subscribe." Urging me to like, subscribe, comment, etc. is an absolutely certain way to ensure I never will.

I don't want to get tied down to any one subject, because so many things are interesting to me, and in the end, I'm not writing for any particular type of reader, but just to write.

That... wasn't exactly true then, and it's not exactly true now. It occurred to me several years ago that some of the best works of fiction were written, not with a particular demographic in mind, targeted to what market research suggests would be the most lucrative audience, but for an individual or small group of people. So, I imagine writing for one particular person. It's not always the same person. Still, it's not a lie; I don't write for a "type."

Thus, I really haven't tried to push myself into a "style." Sometimes I'm funny (or try to be; jury's still out), and sometimes I'm completely serious. Sometimes both at the same time. The problem there is I'm not sure anyone can tell the difference.

This bit hasn't changed.

When I started blogging, lo these many years ago, it was mostly about personal stuff, like the crap I started with today.

Clearly, I still do that when the situation warrants, like when I was traveling and had experiences to relate.

Obviously, I do still talk about personal shit sometimes, but I've arranged my life specifically to avoid drama, so very little happens to me that anyone else would consider interesting.

The downside of this is that when it does, I barely have the practice to handle it.

But writing isn't work. I suspect that if I ever made actual money from it, I'd probably start to consider it work and break out in hives.

Still true.

As I noted recently, I've managed to add an entry every day of this calendar year thus far, and I'm hoping to make it to December 31 (not that I'll stop then, but I do expect to take a couple of breaks next year).

Those breaks didn't happen, and I'm closing in on a five-year uninterrupted streak.

So, I guess, some things did change, but mostly things outside my control.

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