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.

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.

1 Like

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').

1 Like

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.

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

1 Like

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

November 10, 2020 at 12:07am

#998015

Stylish

I find it unlikely that anyone would think I have "style."

PROMPT November 10th

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?

Yesterday, I made my habitual Monday foray to the local taphouse. For anyone who hasn't been following along, I started doing this when the establishment reopened after lockdown -- I don't remember now when that was. May? June? It's only a mile away (or roughly 1.6 km for anyone reading this in a country that doesn't clutch at archaic systems of measurement), so I walk, for exercise and so that I don't have to worry about drinking too much to drive. The caloric effects of the beer certainly exceed any benefits from the exercise, but whatever; I like beer and the walking can't hurt.

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. Also, it's usually pretty empty on a Monday afternoon. I could further reduce that risk by not going out at all, but then there are other risks, like losing my fucking mind.

I've been concerned about continuing this weekly voyage; infection rates are up everywhere, and, to quote the most overrated fantasy series of all time, Winter is Coming. Here in Virginia, October is usually the last hurrah of summery days, and to be sure, there have been a couple of Mondays when the temperature was a bit low for my outdoor-drinking tastes, but today was positively balmy, with the thermometer reaching a decidedly unNovembery 75 degrees (call it 24C for my friends in non-stupid countries).

But that won't last. Though the manager (with whom I'm now on a first-name basis; his name is Sean and he has two kids and would rather be working anywhere else and is taking classes to that end at the nearby community college) did inform me that they're getting patio heaters, which pleases me. Still, I don't know what I'll do when we start getting the inevitable cold days; I don't mind walking in cold weather so much, but sitting on a restaurant patio? No. Well. I'll worry about that after next week, when the temperature should be in the barely-acceptable mid-60s on Monday. Anything less than that, and I might as well be diving off an iceberg.

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. I say "almost," because I have next to no interest in sports, and while I do have an interest in politics and religion, those are minefields that I tend to avoid here -- though that's not a hard-and-fast rule for me.

Still, anyone who's been following along surely knows my primary subjects by now: language, science, finance, philosophy, fantasy/science fiction, psychology, intoxicating beverages, comedy, cats, music, etc., in no particular order. 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.

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.

But insofar as this is a publicly viewable blog, I do keep readers in mind; that's why I tend to steer clear of the Forbidden Subjects, and try to be informative. My favorite comments are those that say some variant of "that's funny" or "I usually learn something." Those make me feel like I've been doing it right. My purpose is not to get other people to agree with me, although it's nice when that happens, but to present my own point of view. But I also appreciate it when someone disagrees with me, because contrary to popular belief (promoted mainly by me), I neither know everything nor am always right, and sometimes I need that pointed out.

It took me a while to get here. When I started blogging, lo these many years ago, it was mostly about personal stuff, like the crap I started with today. At some point, I started writing about articles I found online, and I've been mostly using that format when I'm not doing some blogging challenge or other. 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. Doesn't help that I don't get out much, these days. But whatever I'm doing, I guess it works, judging by that shiny collection of Awardicons and Merit Badges up there. Still, I'm always trying to improve.

Speaking of which, I'm going to get back to handing out Merit Badges at some point. I sent out a batch not too long ago in connection with the October NaNo Prep, though, several of them to regular readers of this blog, and keeping track of who would and wouldn't get CRs from a Merit Badge Mini-Contest is a lot like work. I'm allergic to work.

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. I mean, I still don't know exactly what hives are, but I gather they're something to be avoided. 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). Would daily writing still hold my interest if it were something that I had to do, rather than something that I do for fun? Honestly, I don't know. Getting paid for photography didn't diminish my interest in photography; the rise of digital cameras did that.

So that's it. Not particularly funny, nor particularly informative, but hopefully readable and with a minimum of spelling, grammar, and punctuation errors. I'll try to do better tomorrow.

As usual.

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