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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Kåre Enga in Montana

about 20 hours ago
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

a day ago
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

February 13, 2019 at 12:38am

#951885

Resurrection

Somehow, I managed to delete my entire bookmarks folder dedicated to blog fodder.

In the grand scheme of things, this isn't exactly Ragnarok, but it still pisses me off an inordinate amount.

I could find no way to recover the 35+ links I'd been saving to (mostly) rant about here.

I will allow myself five minutes to properly rage about this.

... ... ... ... ...

Okay, I'm done. Such are the ephemera of online existence. I did remember the last link I added, so that's what we're going to discuss today.

https://longreads.com/2019/02/11/atlantic-city-is-really-going-down-this-time/

Atlantic City Is Really Going Down This Time

There’s no doubt that Atlantic City is going under. The only question left is: Can an entire city donate its body to science?

Now, the site is called "longreads" for a reason, though I found the article worth reading. But I understand if you don't take the time to peruse it. Here's the tl;dr summary:

Atlantic city is boned because of flooding and the casinos that are popping up everywhere along the Northeast Corridor, and they're trying to turn the place into a climate science laboratory.

First let me say that this isn't an opening to debate climate change. Keep that shit on Facebook. I promise you that if you're not a climate scientist, you have nothing meaningful to contribute to the discussion on either side - and I'm not a climate scientist, either. No one's going to change their mind. This is about Atlantic City.

I've said this before, but I don't know where, so I'll risk repeating myself: I've been to Vegas, Reno, and Atlantic City - the major gambling cities throughout all my adult life. Vegas is Vegas; there's nothing else like it in the world, but it has its own problems in the form of Lake Mead being perennially low these days. Reno is so depressing they had to bring Morrissey in to cheer it up (I'm not kidding; the first time I was in Reno I saw a billboard advertising a Morrissey concert). And Atlantic City makes Reno look like Disney World.

The article speaks of a "duopoly" of gambling hubs between AC and LV, but I think they're giving Reno the short stick in that regard; Reno is even bigger than AC, but perhaps it is that city's relative proximity to Vegas that makes them leave it out. It's not even really that close, though - but it's one of my favorite drives, 8-9 hours through mostly empty desert, with the occasional ghost town along the way.

When I first went to a casino in Atlantic City, one of the slot machines there was Monopoly-themed. This amused the hell out of me, as it is well-known that Monopoly was based on Atlantic City's streets, railroads, and other features. The guy who invented it lived there, so the story goes, and made it up to keep him busy during the Great Depression.

Irony is thick on the ground, there.

That casino is now closed, along with several others, and the ones that remain have... issues.

So it will be interesting to see if the place can once again reinvent itself. While I have no moral issue with gambling, I will note that the more desperate a casino destination is, the harder it becomes for them to make a profit; consequently, games become stacked even more in favor of the house. And, as we've seen, in some cases, it's still not enough. They become less about entertainment and more about gouging visitors. Atlantic City is pretty damn desperate.

And yet, take away the glitz and the blinking lights, and it's an interesting little beach town. I'm kind of hoping they do find something to keep them going, before it, too, becomes just another ghost town.

Well they blew up the chicken man in Philly last
Night now they blew up his house too
Down on the boardwalk they're gettin' ready
For a fight gonna see what them racket boys can do

Now there's trouble busin' in from outta state
And the D.A. can't get no relief
Gonna be a rumble out on the promenade and
The gamblin' commission's hangin' on by the skin of its teeth

Everything dies baby that's a fact
But maybe everything that dies someday comes back
Put your makeup on fix your hair up pretty and
Meet me tonight in Atlantic City

Well I got a job and tried to put my money away
But I got in too deep and I could not pay
So I drew what I had from the Central Trust
And I bough us two tickets on that Coast City bus

Everything dies baby that's a fact
But maybe everything that dies someday comes back
Put your makeup on fix your hair up pretty and
Meet me tonight in Atlantic City

Now our luck may have died and out love may
Be cold but with you forever I'll stay
We're goin' out where the sand's turnin' to gold
So put on your stockin's 'cause the night's getting' cold and maybe everything dies
That's a fact but maybe everything that dies
Someday comes back

Now I been lookin' for a job but it's hard to find
Down here it's just winners and losers and
Don't get caught on the wrong side of that line
Well I'm tired of comin' out on the losin' end
So honey last night I met this guy and I'm
Gonna do a little favor for him
Well I guess everything dies baby that's a fact
But maybe everything that dies someday
Comes back
Put your makeup on fix your hair up pretty and
Meet me tonight in Atlantic City

3 Like • Comment

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