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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 10 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 14 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 5, 2020 at 12:23am

#987254

Inspiration and Aspiration

inspirational (adj.): providing or showing creative or spiritual inspiration

PROMPT July 5th

Tell us about someone you find inspirational.

https://www.lexico.com/en/definition/inspirational

Well, I've already mentioned Leonard Cohen too many times this month. I think he, more than anyone else, made me want to attempt this whole "writing" thing.

Springsteen, maybe? Nah, doesn't quite fit the definition. I can like someone's art without having it nudge me into making my own.

Neil Gaiman? Hm. I've deliberately cribbed his writing style on occasion, but I'm not sure that counts, either.

Or I suppose I could pick the person who penned this prompt, because they inadvertently inspired me to write this entry, or Emily

for posting it. But I don't think that really fits the spirit of the prompt.

The problem might lie in the definition, or in myself. See, I'm neither "creative" nor "spiritual." And I've grown to resent the entire concept of inspiration, thanks to pervasive positivity memes on the internet.

Unless you count these

. But no, those images don't actually make me want to create my own; they just make me laugh.

I know lots of people have inspired me to do this or that thing, but just as I almost never do anything for just one reason, I also almost never do anything just because of one person. Like, long ago, when I decided to become an engineer, I couldn't point to any one engineer and say, "that person is the reason I became an engineer." No, it was a combination of things, like seeing locks on a canal and the Hoover Dam and the Brooklyn Bridge and any number of public works projects.

Which is not to say that everything was my idea. Far from it. Like I said, I'm not very creative. No one can do something without all the work that came before. Specifically, I'm thinking of Nikola Tesla, for example, or Isaac Newton, who supposedly said, "If I have seen further it is by standing on the shoulders of Giants." And then he went on to revolutionize everything.

When I was a kid, I think in elementary school, I have vague memories of an awards ceremony at the end of some school year. Like, they'd pick categories and hand out certificates. These days, from what I understand, such things aren't done as much because they leave out too many people, and I guess everyone gets participation trophies. This was also before the concept of "graduating" from elementary school. So anyway, a couple of things from that ceremony stuck in my mind, though I can't swear my memory of that time is all that accurate.

The first one was an award for "perfect attendance." When I was a kid, I'd catch a cold, or worse, at least once a year, necessitating that I stay home and be bored rather than go to school and be bored, and I remember thinking how unfair that particular award was. "Congratulations. You either never got sick, or you came to school anyway and infected the rest of us." At least I'm pretty sure I had the basic concept of germ theory figured out by then. Either way, I thought that was bogus.

But even more bogus, I thought, was someone who got the award for "most improved."

I can see your eyebrows furrowing from all the way over here. "How is that a bad thing?" you're asking.

Well, at least in my little-kid mind, I was going, "Huh. So if I'd started out getting bad grades, then gotten good grades at the end of the year, I could have gotten that award instead of "Biggest Pain in the Teacher's Ass" or whatever. See, I was savvy enough even then to never actually do my best work, and thus stand out as The Nerd. (It would be years before I learned to embrace my inner nerd, but by that time it was too late; I was already a committed slacker.) So I couldn't have gotten the "Best grades" award, but I could definitely have faked improvement over the course of a school year.

The actual award I got was so embarrassing that I don't even remember what it was; I only remember being terminally embarrassed by it.

The point to this rather lengthy digression from the subject is that the person who won that "most improved" award inspired me to always start out shitty so that people could praise me for having improved so much.

I don't even remember his or her name.

And if you don't think that's an important habit to get into, consider the well-known story of Einstein having failed mathematics as a kid. You might say that would make him the "most improved" thinker of all time.

Except that it turns out that the story, like Washington and the cherry tree, is completely fabricated. But it keeps getting repeated anyway, which just goes to show how that it's less important to simply be great, and more important to achieve greatness after having started well below average, so that people will think it could happen to them, too.

That's inspiring, isn't it?

10 Like • Comment • View 8 comments

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