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').

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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.

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

February 5, 2021 at 12:02am

#1003671

Savvy This

Kids these days with their slang...

14 Colonial-Era Slang Terms to Work Into Modern Conversation

Curious, I looked up the word origin for "slang."

Dictionary.com: "mid 18th century: of unknown origin."

M-W: "origin unknown " ... "The first known use of slang was in 1756"

My money's on it being a contraction, s'lang, short for something like "side language" or "short language" or something beginning with the letter s. But until we invent time travel (which won't happen), we'll probably never know.

The point is, this article is about American colonial-era slang, which oddly enough coincides with the same period when the word "slang" appears to have been coined -- but the word itself is probably older, because these things tended to be used in conversation before they were written down (as opposed to today, when we get most of our argot from the internet). And the concept of slang, the use of informal words and phrases in everyday conversation, is surely older than the word used to describe it, and might even be as old as language.

An argument could be made that language depends upon slang to evolve... but I'm not qualified to make or defend such an argument. It's just something to think about.

Anyway, back to the linked article, which is about a year old but what difference does it make?

But the Colonial Period—which stretched from roughly 1607 to 1776, starting when America was just a group of colonies on the east side of the continent and ending with the Revolutionary War and the signing of the Declaration of Independence—was a fascinating but complicated time in which settlers from England forged a proud new identity. These new settlers brought the English language with them when they came, and whenever English finds a new home, it often takes on a new life.

Or as I like to put it, the British invented it, and we perfected it.

1. Kedge

What It Meant: Doing well

I'm feeling pretty kedge today, so this entry isn't going to be too depressing.

Don't worry; I'm not going to list all of them. Just go to the article to see more.

6. Fishy

What It Meant: Drunk

Possibly no one invented more ways to say “drunk” than colonial Americans. Benjamin Franklin alone compiled 200 ways to say it.

Ben Franklin: Still my favorite Founding Father. Sorry, Alex. We always need more synonyms for "drunk." In college, we called it getting cabbaged. Hell, it's a lot like the situation with reproductive organs: one can adapt a wide variety of words for the purpose. "I got writ last night." "After an evening of getting completely astronomical, he almost regretted it the next morning."

Bonus points if the word you adapt for this purpose is in an obscure foreign language. "I'm going to get completely danchu tonight."

Okay, Mandarin is the polar opposite of "obscure." Still. (According to the googles, "danchu" means "to fade out," as in the end of a scene in a movie, or to fade from memory. What? It's appropriate for describing getting plastered.)

9. Savvy, Savey, or Sabby

What It Meant: To know or understand

While we still use this word to mean something like “literate” (computer-savvy), in Colonial times, it was actually used more like the way Jack Sparrow uses it. So you might say, “I don’t want to come to work anymore, savvy that?” According to Merriam-Webster, it’s derived from sabe, which means “he knows” in Portuguese.

I can't be arsed to trace it all the way back, but another source lists Spanish as the origin for this word. There's a similar verb in French, "savoir," "to know," which in at least one of its conjugations is "savez" which is pronounced a little bit like "savvy" only with the emPHAsis on the other sylLAble. I can only assume that what with all of these Romance languages using a similar verb that it came from Latin, because I've forgotten most of the Latin I ever knew.

Anyway, I knew the word long before Pirates of the Caribbean came out. I guess you could say I was savvy.

14. Circumbendibus

What It Meant: Roundabout

Of all the ways to describe something unnecessarily roundabout— like someone telling a rambling story or taking a weird road when driving somewhere—this word, which dates to 1681, might be the most delightful.

I absolutely need to work this into my vocabulary, since a lot of these blog entries are circumbendibus.

Now it's time to get fishy.

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