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.

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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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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.

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October 21, 2021 at 12:07am

#1019759

Sushi

"Journalistic Intentions"

[18+], #6 of 8...

Jiro Ono

If the unthinkable happened, and I had to choose just one culture's cuisine to eat for the rest of my life, it would probably be Japanese. As much as I love Italian, Mexican, French, Thai, and even American, along with many others, I could probably limit myself to Japanese if I had to. And one of the reasons for that is sushi.

I don't remember exactly when I first tried sushi, but I do remember where: a hole in the wall in Greenwich Village, whose name I've forgotten but it doesn't matter because restaurants in the Village have a half-life of approximately five days, so it's most likely gone now. I think I was in my 20s, and sushi was practically unknown where I came from (though at this point, there are a few good sushi restaurants around here, and you can even get something approximating it at the grocery stores).

Sushi is, of course, not the only thing I like in Japanese cuisine, but I have certainly come to expect it at any place that serves anything remotely Japanese in style.

There's an artistry to it, naturally. I've tried making my own, sans the raw fish which I don't trust around here, and it's hard to get it right. (It's a common misconception among us gaijin that sushi contains raw fish -- while it can, the defining aspect that makes something sushi is the presence of sticky, vinegared rice.)

I only have one hard-and-fast rule about my sushi: I never eat octopus, cuttlefish, or squid. They're smarter than I am, and I make it a point to never eat anything smarter than me (bacon is the exception because it's just so damn tasty).

Other than that, when it comes to sushi, I'm willing to try almost anything.

I always said that if I'm ever in the cliché situation of a doctor telling me I have x months to live, I'm going to fly to Japan and eat sushi there. And also drink some really premium sake, as well as the scotch-like 25 year Yamazaki. Hell, I might have to do all that even if I don't have a deadline, but I'll at least wait until the pandemic dies down. Anyway, point is, if I only have x months to live I'd find a chef willing to prepare fugu sushi for me. Fugu, as you might already know, comes from the blowfish, whose liver is deadly to humans and so it has to be prepared just right. Not a chance I'd normally take, but what the hell, right?

Having never been to Japan, though, the best sushi I ever had was in an obscure town on the Oregon coast whose name escapes me and I can't be arsed to look it up. The second best was in Las Vegas, and in the Before Time, I'd go to that restaurant every time I visited that city.

Would I seek out the restaurant featured in the above link? You bet your ass I would. Apparently you can only get there by arranging it through the concierge of a luxury hotel.

. I'd absolutely do that, even if the place has by that time been passed down to Jiro Ono's son.

And now I'm really craving sushi. The third-best sushi I ever had was right here in my town, at a place called Ten. I think it's called that because it costs ten times as much as most other restaurants. But it's totally worth it, and I think I'm going to have to visit again soon.

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