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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Write_Mikey_Write!

about an hour 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 3 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').

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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.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

May 6, 2023 at 1:18pm

#1049296

Enter the Dragon

I haven't been feeling like going to the movie theater for a while (which is why I haven't done any reviews recently). So I missed the D&D movie. This article is from around the time that film came out, and I read it anyway because I'm a gamer.

14 Fun Facts About Dungeons & Dragons
Before watching the new movie adaptation, here’s what you need to know about the history of the fantasy role-playing game

Of all the publications I'd have guessed would write a retrospective of a role-playing game, with or without a movie tie-in, Smithsonian would be near the bottom of the list, right around the same spot as Proceedings of the International Society of Metallurgists.

(I just made up that last one)

But this is the timeline we deserve, so here it is.

In the early 1970s, Gary Gygax lost his job at an insurance company in Chicago.

Never says why. I'm going to go with "fired for being a dick."

Living with his family in Lake Geneva, Wisconsin, he started working as a cobbler as a replacement gig. But money was tight, and his children had to put cardboard in the bottoms of their shoes instead of buying new pairs.

You had SHOES? Luxury!

Little did Gygax know that his luck would soon change. Dungeons & Dragons (D&D), the fantasy role-playing game he co-created with Dave Arneson, became a national phenomenon.

That may be overstating the case. National, sure. Widespread? Took a while.

Since its debut in 1974, D&D has only grown in popularity. No longer a niche game, it’s been played by more than 50 million people to date, according to Wizards of the Coast, the Hasbro division that owns D&D.

I played it before it was cool.

Incidentally, Hasbro also owns Ponies. I want to see a D&D ruleset that's set in the My LIttle Pony universe.

What? No, I'm not a brony. I just think it'd be hilarious.

Starring Chris Pine, Michelle Rodriguez and Regé-Jean Page of “Bridgerton” fame, Honor Among Thieves is set in a fantasy D&D world. It follows a band of thieves who attempt to recover their loot from an ex-member of their crew, who betrayed them and used magic to seize control of the kingdom.

So, basically, The Italian Job (2003), but with fantasy.

No, no, it's fine. That's one of my all-time favorite movies.

In honor of the game’s turn on the silver screen, as well as its upcoming 50th anniversary in 2024, here are 14 fun facts about the history of D&D and the people who made it.

It's not the first time they've tried to adapt D&D to movies. The last attempt was... how do I put this charitably?... a giant steaming pile of owlbear shit.

Anyway, obviously, I'm not going to go over every one of the "fun facts" (some of them aren't much fun at all). The link's up there if you're interested.

Mostly, I just want to highlight the stupidest one.

8. In its heyday, D&D sparked a moral panic.

In the late 1970s and early 1980s, D&D entered the national spotlight under unexpected circumstances. Critics—many of them religious fundamentalists—argued the game was corrupting America’s youth by promoting devil worship, witchcraft and violence.

First, it was hardly unexpected. One early book had a naked boob on its cover (I think it was called "Eldritch Wizardry.") That's a sure way to get fundies to shriek at obnoxious volume.

Second, the real reason a lot of these assholes protested was because the game favors cooperation and imagination, not competition and some kind of ball.

Third, and this should go without saying but apparently it can't, none of the allegations were true. It's a game. Yeah, there was a lot of emphasis on a few people who played it who committed suicide or whatever, but conveniently left out were all the people who played, say, football and committed suicide. Or were bullied and committed suicide. Or were gay in the 1980s and committed suicide. Take any group of people who share any interest whatsoever, and you'll find both suicides and antisocial/illegal behavior. That doesn't mean there's a correlation.

And finally, TSR (the publisher at the time) couldn't possibly have done a better job advertising the product:

Repeatedly debunked by researchers, the supposed link between D&D and violence earned the game a bad reputation in the eyes of some—but as Clyde Haberman noted for the New York Times in 2016, it also boosted D&D’s popularity, “with the numbers of players leaping from the thousands into the millions.”

12. The most recent version of the game is the fifth edition, published in 2014. A new edition is on the way.

I've played 1st, 2nd, 3rd, and 5th editions (I looked at 4th and went NOPE). I have no idea what 6th is going to look like, and the way WotC has been acting recently, I'm not sure I want to.

There is an alternative. Whoever was running things when 3rd Edition came out (I think this was right after WotC, better known for Magic: The Gathering, acquired the rights) based the rules on an open-source system. So another company, Paizo, took that ball and ran with it (to mix game metaphors), creating Pathfinder, which had a ruleset very similar to 3rd Ed. D&D. More recently, they overhauled the rules again to create Pathfinder 2nd Edition.

I'm currently playing in a sort-of weekly game (through the magic of teleconferencing) of Pathfinder 2nd Edition, which I find to be a great deal of fun.

And isn't that what we play for?

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