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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 2 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 4 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.

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.

August 21, 2022 at 12:04am

#1036756

A Fine Selection of Bumfodder

I'm not above making up words if I don't know a good one for the context. Or even just for fun. None of them have caught on, but English has some words that caught on for a while, and then... caught off?

56 Delightfully Unusual Words for Everyday Things

If your dream is to talk like Moira Rose from Schitt’s Creek...

Who? No.

...look no further than Mrs. Byrne’s Dictionary of Unusual, Obscure, and Preposterous Words, one of the dictionaries Catherine O’Hara used to tweak her iconic character's lines.

Still not interested in the show.

The following terms for everyday things are ones you'll want to add to your lexicon ASAP.

People who grew up with the internet seem to think they had the monopoly on turning words into acronyms. They did not; ASAP predated widespread use of computers. Some sources claim it's about a hundred years old They also didn't invent weed or sex. Just saying.

On the other hand, a bunch of words that people think were acronyms weren't. Those are called backronyms because people love portmanteaux (I, on the other hand, do not). An example of a non-acronym is the ever-useful F word.

Anyway. The article lists too many words for me to copy all of them, and besides, lawyers exist. So I'll just highlight a few.

3. Baragouin

Another word for gibberish that dates back to the early 1600s.

But why bother? Gibberish is easier to spell, pronounce, and remember, and also has the advantage of sounding like what it is.

4. Bumfodder

Why yes, this is a 17th-century word for toilet paper.

Again, easier to say "bumwad," or even "loo roll" if you're of a British bent.

9. Clinchpoop

If you get into a confrontation with a jerk, consider calling them a clinchpoop, which the OED defines as “A term of contempt for one considered wanting in gentlemanly breeding.”

I mean, sure, hit 'em with that word if you want them to hit you with their fists.

13. Eructation

A fancy word for belching...

Everything sounds more proper when using Latin root words. That's one reason we have so many. Defecation. Urination. Flatulence. This one, though, is just showing off.

18. Forjeskit

“Forjesket sair, with weary legs,” Scottish poet Robert Burns wrote in 1785’s “Second Epistle to J. Lapraik.” It was the first use of the word, which means “exhausted from work,” according to Mrs. Byrne’s Dictionary.

Still no definitive word on whether Scots is a dialect of or sister language to English, but I'm pretty sure this word belongs in that language. That's not the only Scots word at the link.

24. Join-hand

Another word for cursive handwriting.

Some words went obsolete for a reason.

31. Maquillage

Another word for makeup that dates back to the late 1800s.

And that one's French. Yes, English stole a bunch of words from French, but most of them came from way before the late 1800s.

32. Matutolypea

According to Mrs. Byrne’s Dictionary, this term means “getting up on the wrong side of the bed.” Macmillan Dictionary notes that the word “is derived from the Latin name Matuta from Matuta Mater, the Roman Goddess of the dawn, and the Greek word lype meaning 'grief or sorrow.’”

Unnecessary. Cumbersome.

40. Ombibulous

According to Mrs. Byrne’s Dictionary, ombibulous describes “someone who drinks everything.” It was coined by H.L. Mencken, who once wrote, “I am ombibulous. I drink every known alcoholic drink and enjoy them all.”

Finally! One I have reason to steal.

47. Scacchic

“of or pertaining to chess,” according to the OED.

As far as I've been able to figure out, the French word for "chess" is the same as the French word for "failure." Unsurprisingly, it seems to be related to this one, which comes from Italian.

51. Tapster

Another word for a bartender.

Hey look, another one I can actually use.

Anyway, like I said, many more at the link. Personally, I think most of these, however unusual, have better words to describe their concepts. But some writers seem to take great delight in vexing their readers with obscure synonyms, so the article might be useful to them.

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