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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 13 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 17 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.

July 31, 2020 at 12:01am

#989563

Where Jokes Go to Die

Let's get serious about comedy for a few minutes.

https://www.cracked.com/article_28266_5-famous-jokes-everybody-manages-to-screw-...

5 Famous Jokes Everybody Manages To Screw Up

Or -- possibly more accurately -- Cracked Screws Up Famous Jokes.

Jokes are the most important form of communication we have, and many are strongest the moment they're first told. Some get even better with repetition, and many are repeated till a single line turns into a hollow husk of a catchphrase that people apply endlessly, with all the original genuine humor lost.

Oh, I don't know. The most important form of communication we have? That would be when we meow back at our cats.

5. "It's One Banana, Michael. How Much Could It Cost? Ten Dollars?"

I'm pretty sure I've never heard this one until I read this article. I even had to follow the link, which told me it comes from Arrested Development -- a show I've always had less than zero interest in watching.

As it was the first time I heard it, you would expect, via Cracked Comedy Theory above, that I would have found it hilarious. I didn't. Mildly eye-rolling, maybe. Perhaps I would have had to understand the characters and context better.

Anyway, they bury the joke in the ground and shovel dirt over it by going on to explain it.

4. "Shut Up And Take My Money!"

Hey, I know this one. I use it myself.

Did that amazing new game get announced, and you want it right away? Or some shiny and whirring new bit of electronics? How about a proposed invention, something that might never even really come into being, but you need it, and you need it now? Only one GIF can sum up your feelings.

Hey I can do gifs too!

In the show, Fry isn't saying this about a good product. He's saying it about a bad product. The joke isn't that he's already sold on it, so he shushes the salesmen from talking it up further. The joke is that he's already sold on it, so he shushes the salesmen from explaining the bad item's flaws.

But you know what? It doesn't matter. Sure, maybe it's overused, but the mark of a good quote is that it can be used in other situations than the original writers intended. Stop telling me how to get mileage out of other peoples' creativity, Cracked. You're not my supervisor!

3. "Up To Eleven"

Okay, now you're treading on sacred ground. I'm pretty sure that this line from Spinal Tap is the most successful reference joke of all time. It has embedded itself into pop culture even more thoroughly than quotes from Star Wars, and you can't swing a lightsaber without slicing a Star Wars reference joke.

Just to give two examples of how thoroughly that single line has taken root and become part of the everyday lexicon: First, the IMDb page

for that movie has a star rating system that goes to 11. So okay, that's only to be expected, right? But that brings me to the second example: The BBC, the oldest public service broadcaster in the world, with a stuffy British management not exactly famous for its sense of humor, has its own proprietary video player on its web pages -- and its volume slider goes to 11.

No, of course "but these go to eleven" isn't funny anymore. It's too pervasive. What it is now is an idiom. And regardless of how it was used in the movie (which I first saw when it came out and recognized that scene as pure comedy gold), we can use it however we like. Cracked trying to comedysplain to us how it was supposed to be used is like... well, it's like those pedants who insist that you can't split infinitives or end sentences prepositions with.

2. "You Keep Using That Word, I Do Not Think It Means What You Think It Means"

You keep using these jokes. I do not think they mean what you think they mean.

Seriously, you're supposed to be a comedy site. Lighten up, Francis.

1. "Nobody Expects The Spanish Inquisition!"

Now, here, the discussion of this one actually makes some sense:

The basis for the sketch is the phrase "I didn't come here expecting the Spanish Inquisition," a facetious way of pointing out someone's questioning you more intently than is reasonable. Type that line into Google, and from the search results, you'd swear that Monty Python invented it. But it was already a common figure of speech before the sketch.

Which I didn't know, because the Spanish Inquisition sketch was basically before my time. It predates even Spinal Tap by something like 15 years. In other words, its original meaning has been superseded by the Python reference.

In conclusion, yes, some lines get overworked. It is, for example, impossible to make any comment, serious or otherwise, about deep philosophical questions such as: What's the meaning of life? What's the ultimate answer? without someone shouting out: FORTY-TWO!!! It gets tiring, and it's caused me to stop talking, or even thinking, about such deep questions.

Probably for the best, anyway. I'd already figured out that comedy is the true Meaning of Life.

13 Like • Comment • View 9 comments

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