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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Adherennium Plotting something

about 2 hours ago
In response to "Global Domination"

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

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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.

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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.

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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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May 5, 2024 at 7:04am

#1070539

Revisited: "Fail"

We're going back in time, as usual for Sunday mornings. This time, it's just to October of 2020 (specifically, 10/10/20, one of the few dates that work in both American and European style conventions and which can also be turned into a mathematical equation): "Fail"

I did the entry for that month's round of "Journalistic Intentions"

[18+], which is still an active blogging challenge, though not every month. Also, all the links in the entry are still solid, which isn't too surprising for something less than 4 years old.

Anyway, I got curious and looked up the origin of the name Fail.

I didn't go into this at the time, but today, I noticed that the ultimate origin of the Scottish surname Fail (which has many alternative spellings) is the name Paul. Don't ask me what kind of linguistic vowel shifts it takes to get from Paul to Fail; I don't know. But the name Paul, from Paulus, is Latin in origin, though it is probably most associated with the Paul of the New Testament.

So Paul becomes Phaill (or some similar spelling), and, by the convention of some Scottish clan names, generates MacPhaill, later Anglicized as MacFail or just Fail.

At least, that's one possible explanation. I never did trust some of these genealogy websites. But you know the Meat Loaf character in Fight Club? "His name was Robert Paulson." Well, "Paulson" is the English equivalent of MacPaul, which we've already speculated became the name Fail, so I have to wonder if Palahniuk did that shit on purpose. Probably not; his symbolism tends to be more of a, well, a punch in the face.

Anyway, back to my original entry:

I know, I know, it's rude to make fun of peoples' last names. You should be proud of your last name, even if it's Fail.

Or Hogg, as in yesterday's entry (coincidentally, also Scottish). Still, being proud of being a Hogg (or a Fail, for that matter) is no damn excuse to name your kid Ima.

There's the story of a Dr. A. Hedgeh, for example, who apparently had a problem with people adding "og" to his nameplate.

In case you don't want to bother rereading my 2020 entry, I'm including that link

here again, because I still laugh every time I see it. Fake or not.

So, yes, it's rude to make fun of peoples' names.

But sometimes, it's so funny you can't help it.

3 Like • Comment • View 1 comment

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