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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Write_Mikey_Write!

about 6 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 8 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

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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.

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').

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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.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

May 9, 2021 at 12:05am

#1009897

La Langue

PROMPT May 9th

Write about language - What languages do you wish you could speak? What’s the most pleasant sounding accent? What’s the funniest word in the English language (or your native language)?

Periodically, someone will come up with a "longest word in the English language" essay, probably because they're not being paid by the word but by the letter. Almost inevitably, the winner will be declared to be "floccinaucinihilipilification" or "antidisestablishmentarianism," the former of which means, roughly, "making a big deal about nothing." Which is appropriate, because English is largely arbitrary, and if that word were truly necessary, we Americans at least would shorten it to "flok" because why pronounce such a long word when we could use the time to stuff another Big Mac into our maws?

Incidentally, I may have a shit memory, but I typed those words without Googling them. I can't promise they're spelled correctly, because my browser doesn't recognize them. Which means they're not actually the longest words in the English language; if Firefox doesn't know it, it's not English.

In any case, neither word sees everyday use; the only time I ever see them is in "longest word" articles. Some of said articles are quick to point out that there are even longer words, but they qualify as technical terms. Those I don't remember as vividly, but as I recall they're from chemistry.

Chemistry was heavily influenced by the German language, which I don't know a whole lot about, but which I understand is very good at stringing a lot of short words together to make a mega-word. Which, again, is appropriate, since a big molecule is a bunch of short molecules strung together to make a mega-molecule. Though English is technically a Germanic language, most of our vocabulary (about 60%, if I recall correctly) comes from Romance languages, largely through the influence of French. And Romance language words just don't have the same stringthemtogetherabilityness.

Point being, "longest word" and "funniest word" are both pretty arbitrary, and at some point all you're doing is making shit up. Which, I suppose, is how language works in the first place. I mean, no name for a thing or action, no words that modify things or actions, no word at all, is an intrinsic property of the thing, action, or modifier. A case could be made for those words that are onomatopoeic, like "buzz" or "meow," in terms of them being intrinsic to the things they describe, but given that those words are different in different languages, it all comes down to how we interpret the sounds.

Apropos of nothing, I've actually been to Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch, in Wales, which may or may not be the longest place name in the world. Put that on a map of the planet, and it will either start in Canada or end in Russia. That's not English, though. It's Welsh. Never call Welsh "English," lest you invoke the wrath of actual Welsh people. Then you might get a sheep thrown at you.

I did have to look that one up, incidentally.

As you can tell, and as you know if you've been following along, I kinda love linguistics. I don't know nearly as much about it as I'd like to. Given that the only other language that I have any facility in whatsoever is French, and that only on a beginner level after nearly two years of practice, it's difficult for me to engage in too much comparative linguistics. I used to know some Hebrew and Latin, but the funny thing about language is if you don't use it, you lose it. Unless, I suppose, you have a much better memory than I do.

Speaking of French, even before I started learning it full-time, I always thought it was a very pleasant-sounding language. Probably not when it's being shouted at you from across a battlefield, but in other situations. I mean, compare the sound of « Voulez-vous coucher avec moi ? » with its rough English translation, "Wanna bone?" and you'll see what I mean.

But no, I'm not learning French so I can pick up French chicks. I'm too old for that merde. (But, still, I wouldn't say non.) I'm learning it so I can drink wine in France and beer in Belgium.

One language that I've wanted to learn for a long time is Russian. Of course, with the political climate today, that would probably get me put on a List somewhere. And I've found that I'm terrible at learning more than one language at the same time. Hell, I'm not that great at learning one language at the same time.

But it's not going to stop me from trying.

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