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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 22 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.

July 14, 2020 at 12:17am

#988106

It's a Trappist!

Godsdammit.

PROMPT July 14th

If you won a free trip to any foreign country, all expenses paid in your own private jet and had the time to go (and there were no travel restrictions due to a global pandemic

), what is the first foreign country you would visit? Who would you bring with you? What would you spend your time doing?

Now? I'm going to do this prompt NOW?

I've said some of this shit before, but I'm going to say it again for any new readers, and because I'm fucking pissed. In the American sense, not the British.

Last year was my mostly-stay-at-home year. Not only did I want to conserve money for upcoming trips, but I wanted to lose weight so I wouldn't look like a typical American.

I was mostly successful at both.

The plan was to go to Scotland in May with a friend for the Islay festival. One tiny island, nearly a dozen Scotch distilleries. My friend ghosted me. Covfefe-19 happened. I didn't go to Scotland. Still, this was supposed to be the year I cut loose a little bit, traveled more, saw more movies in theaters, that sort of thing. Damn this pandemic to the fires of Oblivion.

I have plans to visit Belgium next year with my friend Artemismad

. For that, I'm learning French. If I feel like I can understand that language, I'll also try to learn some Dutch. As a bonus, that means I could get by in France and the Netherlands also. Yes, I know that a lot of people in all those countries know English. That's no excuse; I refuse to be known as "the ugly American." This shit will not be resolved by next year. So I doubt I'm going to Belgium or France. Or Scotland. Or the Netherlands. Or Belize. Or even travel in the US.

I'm prone to depression and this shit is not helping. Not the pandemic, not the travel restrictions caused by the pandemic, and certainly not prompts like this one. The only thing I have to look forward to these days is travel and death, and it looks like the latter is going to happen before the former.

Even if I somehow manage to stay alive and reasonably healthy (unlikely), my passport will probably expire before I get a chance to travel again. And I haven't even used it since I last renewed.

So you'll excuse me if dreaming about travel just makes me ranty. I'm generally a stay at home type, but what keeps me going, what keeps me from sinking into the dark depths of depression is a) booze and b) knowing that I can travel to try exotic booze.

At least I still have (a). For now.

The countries I mentioned are not my only desired destinations, but I try not to think of the others, so I'm going to stop myself right here.

As for the prompt, ask me last year and I would have said "Scotland." And I still want to go to the Islay festival at some point, with someone who appreciates the world's greatest whiskey. Or whisky. I forget which countries spell it which way. After a few it won't matter anyway.

But right now? In the utterly impossible scenario above? Belgium. With my friend, as I mentioned, and whoever else wants to go. Primarily, I'm interested in immersing myself, at least figuratively, in Belgian beer. Trappist ales, saisons, whatever. I can get some of them here -- I just had a nice couple of bottles of Delirium Nocturnum yesterday, and there's still one in my fridge along with a big bottle of Kwak -- but as with California and wine, they keep the really good stuff for themselves.

And then there's the food. Ever seen the Belgian flag? I'm pretty sure it's a representation of chocolate, beer, and waffles. Belgium is the one country that out-Frenches the French when it comes to cuisine.

But, contrary to popular belief (that I encourage), I can't eat and drink all the time. I'm curating a list of Belgian sites I want to visit. Here are a few:

Musée Hergé, a museum dedicated to Belgium's most famous non-consumable export:
https://www.atlasobscura.com/places/herge-museum

Speaking of Belgian beer:
https://www.atlasobscura.com/places/delirium-cafe

The most metal sculpture in existence:
https://www.atlasobscura.com/places/the-atomium-brussels-belgium

That Damme Canal:
https://www.atlasobscura.com/places/damme-canal

"Yes, I'd like to visit the Hergé museum and also this one. Why are you looking at me like that?"
https://www.atlasobscura.com/places/torture-museum-bruges

Because why not:
https://www.atlasobscura.com/places/tour-cybernetique-cybernetic-tower

"According to this bar, God gave an '11th commandment' to Antwerp: Thou shalt drink beer."
https://www.atlasobscura.com/places/elfde-gebod-eleventh-commandment

Yes, those are all from Atlas Obscura. I have at least a dozen more of them saved. I go to that site when I want to torture myself with dreams of places I can't freaking go to right now.

Grrrr.

Now I'm all depressed again. Maybe I'll open that last bottle of Nocturnum.

8 Like • Comment • View 10 comments

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