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 9 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 11 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.

June 9, 2021 at 12:07am

#1011528

Language Barrier

Entry #3 of 8 for "Journalistic Intentions"

[18+] - as usual, I pulled this one at random, but honestly, if it hadn't, I'd probably cheat by making it my eighth entry anyway.

Education, education, education

The differences between US and UK terminology and society have been an interest of mine for a long time. When I was a kid, lo these many years ago (but still after the Revolution), I read both American and British childrens' books. This led to a good bit of confusion, some of which persists to this day.

I've also been known to use British idioms from time to time, like when I say I can't be arsed to do whatever. I do generally use American spellings of words, though some spellings probably slip through. For instance, I'm pretty sure I've used both "canceled" and "cancelled," the latter of which is generally British. Still, I don't have a colourful sense of humour.

Now, I've joked in here before that they invented this language, but we perfected it. Just to be clear, that is, indeed, a joke. But it does help to have a bit of guidance on the differences. Most famously, probably, Rowling changed one of the books in her famous series from "Philosopher's Stone" to "Sorcerer's Stone," apparently specifically because American kids would think of old boring guys with beards if the former were used. (To be fair, most philosophers were old boring guys with beards, except for Neitzche who had an epic mustache, and Camus who wasn't old and kept his face shaved).

Personally, I think the world would have been a better place if they didn't have a separate Freedom Edition of Potter, but instead took the opportunity to introduce the little brats to UK English.

And yes, I know Rowling is cancelled now. Or was she canceled? I can't keep it straight.

Like I said yesterday, I'm currently going through the source material before going to see Cruella on Thursday. Disney has long had a... difficult... relationship with British stories, and the Dalmatians movies are no exception. Still not as cringeworthy as Mary Poppins, though. Point is, I hadn't seen the 1961 cartoon since like 1970, and I'd never bothered with the live-action 1996 remake, which, apart from Glenn Close doing her best "The Devil Wears Pongo" impression, Hugh Laurie being Hugh Laurie, and a bunch of disgustingly cute puppies, turns out to be fairly unremarkable. In any case, the movies reminded me that I'd read the actual 101 Dalmatians book (with the numbers spelled out, which I can't be arsed to do) way back in my misspent youth, and it was one of the works of fiction that introduced me to Britishisms.

Incidentally, I'm not bothering with any of the sequels, and I don't hold out much hope for Cruella. I mean, I get her as a villain? But this trend toward glorifying the Bad Guy (or Gal) is rather off-putting. She's a puppykiller, for fuck's sake -- perfect antagonist material, as long as she doesn't actually get her way. What's next, are we going to get a movie with a pedophile as the protagonist? (Yes, yes, I know, Lolita, whatever -- no one in that movie was a sympathetic character, not even the girl or Jeremy Irons.)

Where was I? Oh, yeah, the video above. Look, I know it can be a pain in the ass (or arse) to click on all these embedded videos, but that one's worth a watch. The guy in the video at first seems like some updated version of Alistair Cooke from Masterpiece Theater, but it's all a cover for a dry British wit (which is almost as good as dry British gin), while at the same time being, well... educational.

And if you're reading this blog in the first place, I can only assume you like a side of humo(u)r with your facts and my opinions.

The ultimate point here is: yes, the US and UK educational systems are different. But both seem to work, so why bother comparing them? Well, partly because almost all knowledge is worth having, but also partly to foster better cross-pond communication. After all, as the narrator points out (paraphrasing Shaw, apparently), we're separated by a common language.

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