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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February 7, 2021 at 12:02am

#1003870

Moral Panic

Kids these days with their... um... kid stuff.

Video Game Hysteria News Report from 1982 Shows How Much The Media Scared Us

The one constant across all of human history is the older generations freaking out over something that the younger generation is doing.

They [Young People] have exalted notions, because they have not been humbled by life or learned its necessary limitations; moreover, their hopeful disposition makes them think themselves equal to great things -- and that means having exalted notions. They would always rather do noble deeds than useful ones: Their lives are regulated more by moral feeling than by reasoning -- all their mistakes are in the direction of doing things excessively and vehemently. They overdo everything -- they love too much, hate too much, and the same with everything else.
(Aristotle)

More complaints about "kids these days" from millennia ago can be found here.

Anyway, the Cracked article linked first above.

Once upon a time, there was a world before Fortnite, COD, and even Angry Birds when most people needed to visit arcades and other public places to get their video game fix.

I was one of those kids in 1982.

Yet instead of enjoying their time outside of the house, socializing at arcades as they gamed with their friends, basically, everyone and their mom thought that video games were actively destroying their brains, sparking mass hysteria among parents.

And before that, it was hippie stuff, and before that it was jazz, and before that it was... I don't know... writing, maybe. Or revolutions against colonial oppressors.

"GRONK! FLASH! ZAP! Video Games are Blitzing the World!" read a cover of Time Magazine in 1982.

On the other hand, maybe it did destroy my brain; I have a distinct memory of Pac-Man being Time Magazine's "Man of the Year" (before they finally stopped being so fucking sexist about these things), but in researching this blog entry, it seems that the Pac-Man "Man of the Year" cover was actually a spoof done by Mad Magazine. Mad, of course, was Cracked's main rival at the time, but more importantly, it was published by the same people who published Time.

Everything is connected somehow.

Time did, however, once select "the personal computer" or something similar as "Man of the Year," notably before they changed it to "Person of the Year," thus illustrating that to people back then (People was a popular magazine then too), the computer was more important than the wimmins.

In an attempt to curb this "electronic blight," with 4,000 to 5,000 consoles popping up in arcades, pizza parlors, grocery stores, and drugstores, city officials passed regulatory laws, only allotting video games in commercial or industrial areas. Because nothing says good, wholesome fun like a bunch of unsupervised children heading down to their local factory district area to play some Pac-Man, right?

Also, I don't remember any of this. I got my video game fix in arcades and at the local 7-Eleven.

"Officials say they are responding to complaints from parents that children have skipped school or stolen money to play the games and made a nuisance of themselves," the anchor said over footage of kids seemingly having a great time playing games.

Said 7-Eleven was located right across the road from my high school. I'd leave extra early in the morning to stick stolen quarters (okay, they weren't really stolen, but it's not like I had a job at the time) into Ms. Pac-Man and/or Galaga prior to trudging over to prisonschool.

I got really, really good at Galaga, by the way. When the first Avengers movie gave it a nod, I might have cheered right there in the movie theater.

I don't recall that I ever skipped school just to play video games. But I can't say I never played video games when I skipped school. It's just that the owners of that particular convenience store were narcs, and if a kid was there during school hours, we'd get told upon.

Incidentally, I had occasion to pass by that high school fairly recently, because it was on the way to a microbrewery I wanted to try -- I think this was in November of 2019, because it was definitely in the Before Time, but still recent -- and behold, there is still a 7-Eleven across the (now four-lane) road from the high school. It does not, however, still house video game consoles, but the cashiers still looked like narcs. This shouldn't be surprising, since that convenience store is also next to the FBI Academy. Yes, that FBI Academy; it's right across the line from Quantico.

Point is, there have always been things that kids do that freak adults right out. This, I think, is an important part of childhood, and I hope it never changes. Because, it's not in spite of these moral panics that civilization keeps right on chugging along, at least for now.

It's because of them.

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