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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 16 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

about 21 hours 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

a day ago
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 2, 2019 at 12:31am

#950956

Hav-a-Tampa

https://www.tampabay.com/visual-arts/top-things-to-do-in-tampa-bay-for-saturday-...

Now this... this is more my speed.

Full disclosure: I had ties to Tampa. My uncle lived there (died in the early noughties). He was kind of a big deal there, has buildings named after him and shit. Nice place. Never snows. Oh, sure, you get the occasional hurricane, but what place is completely safe?

Sadly, I haven't had a chance to go back since his death. I need to - there are a lot more breweries there, now, and plus there's this:

https://yborcityonline.com/

And this, across the bay:

https://thedali.org/

And of course, these:

https://foursquare.com/top-places/tampa/best-places-cigars

People are always asking me about Cuban cigars, since I make no secret of my hedonism and decadence. We still can't legally get them in the US - stupid embargo that long ago outlived its usefulness. But of course, Florida has a thriving Cuban population, so you get things like Ybor City, above, and one of Tampa's major beer factories is called Cigar City Brewing.

Don't tell my government, but I've had Cuban cigars anyway. I've visited Canada and the UK and purchased (and smoked - couldn't risk schlepping them back to the US) them there. And I'm here to tell you: Cuban cigars aren't all that.

Supposedly, when Kennedy initiated the embargo, he filled a giant humidor with Cuban cigars before anyone else knew the embargo was to take effect. The perks of leadership, I suppose. You know where that got him. I have no idea what happened to the cigars. Possibly, Johnson smoked them all. I like to think it was Nixon.

But since then, the major manufacturers and growers have gone to places like the Dominican Repulic, Guatemala, Nicaragua... and Florida. What we get from them is every bit as good, possibly even better, than what comes out of Cuba. Hell, there are excellent sticks coming out of India. The only things left of the Cuban cigar legacy are those smokes, and for people in the US, a cachet of lawlessness that surrounds the very idea.

I'm not a fan of Florida in general. I mean, look at the place on the map - what is it, but the Wang of America? (Yes, I got Elisa the Bunny Stik

, who wisely moved out of the state, to start calling it that.) And the Keys are... well, let's just say the place could use a few antibiotics. Disney World is like a giant chancre sore in this metaphor, as are The Villages, a sprawling retirement community about an hour north of Orlando where golf carts have the right-of-way and the houses all look like they only need one good Cat I hurricane to end up in the Gulf. So, there's no danger of me joining the herds of other retirees living there.

Doesn't mean I don't want to visit again.

I'll end this with a joke. It's an old one, and I'll try to render it faithfully. I promise it's relevant on a couple of levels:

Guy dies and goes to Hell. One of the demons notices that, despite the high temperatures, he's smiling all the time, so he reports to his Dark Lord. Satan goes up to the guy and goes, "You know you're in Hell, right? It's as hot as... well, it's hot here. Why are you smiling?"

"Well," says the guy, "This is just like back on the farm in August. I'm used to it."

So Satan puts him, alone, in an even hotter place. But a week later, he's still smiling and laughing.

"This is Hell," Satan reminds the guy. "You're supposed to be tortured here. What's with the smiling?"

"This is just like being in the silos back home," says the guy.

So Satan leaves and turns to the demon in charge of solitary confinement: "Okay, turn the heat all the way down."

So a week later, it's sleeting and icing up in there, and Satan looks in to see the guy laughing and dancing a jig, occasionally throwing his arms up in victory. "Dammit," he says. "What does it take? And don't tell me this reminds you of your farm."

"Look around you," the guy explains, smiling and gesturing expansively at all the ice and snow. "The Bucs have won the Super Bowl!"

3 Like • Comment • View 2 comments

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