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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 20 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 22, 2020 at 12:02am

#988828

Vice-Virtue

Oh boy. Minefield ahead.

PROMPT July 22nd

Make a list of the top five most important virtues and why.

I looked at this site

to help me remember what some virtues are called.

Some of those below aren't on that list. As always, ask me another time and I'll have different answers; consistency is most definitely not one of my traits. So without further disclaimer, my Top 5 Most Important Virtues, in order, as of right now.

5. Humor. I find it important to have a sense of humor, because it's better than sinking into the abyss of despair. By finding humor in absurd situations, I can maintain a clear head and keep things in perspective.

4. Flexibility. We humans are characterized by, among other things, our ability to adapt. Failure to do so rejects what makes us human just as surely as lacking a sense of humor does. I'm stubborn about a lot of things, but when new information comes in, I adjust my actions and worldview accordingly.

3. Reliability. It's important, I think, to keep one's commitments. So much so, in fact, that I'm averse to committing to anything, because my flexibility means that if circumstances change, I change as well. But once I make a commitment, I do my damnedest to follow through. This is not just so that other people can benefit, but also as a matter of self-respect.

2. Curiosity. Another human trait is curiosity; that is, the desire to know things and figure out what makes things work. This is the basis for science and philosophy. To me, it's important to always be learning. This also means the desire to try, and to experience, things that are new to me.

1. Fairness. The world is fundamentally unfair. This should go without saying. People who do horrible things are often rewarded, while those who do great things can be overlooked. It's necessary, then, to be as fair as I can be, and not treat people differently because I'm in their tribe or clan or whatever. The world being unfair is often used as an excuse by crappy people to be unfair themselves; this misses the point entirely.

And now, just because I can, I'm also going to list my Top 5 Things That People Think Are Virtues, But Really Aren't:

5. Tolerance. I mention this because tolerance simply doesn't go far enough. I don't want to be tolerated; I want to be accepted. I assume others are the same way. That doesn't mean I'm not going to snark at you if you like to drink Coors Light instead of real beer, but at base, I accept that people are different from me and that it's a good thing. Diversity is strength.

4. Faith. This is going to piss some people off, I know. I define "faith" as "belief in something with little to no evidence for it." Think aliens are going to come save us from ourselves? No evidence. Think God is just and loving (or even exists)? No evidence for it. Think your life is going to work out just fine? No evidence for it; in fact, all evidence points to us all dying at some point. Faith negates curiosity and learning. Faith makes people susceptible to manipulation. Faith is complacency. No thanks.

3. Productivity. I mean, seriously, people, this has become the secular capitalist religion of choice these days. It boils down to working harder and/or smarter to enrich your bosses. "How to Be More Productive." "Productivity Tips & Tricks." "Productivity for Dummies." Screw that. Live your life.

2. Temperance. Related to the above, sometimes indulgence is good for one's mental health. As Heinlein put it, "Everything in excess. Moderation is for monks."

1. Continence. By which I mean the definition with sexual connotations. People are just too damn prudish. This of course doesn't mean forcing your will on someone; that's clearly wrong. They talk about "consent." As with tolerance, consent doesn't go far enough. How about some enthusiasm? Sex is part of life, and one of the biggest lies foisted upon us was the idea that it's sinful. No. It's only sinful if it hurts someone; hence the "enthusiasm" part. Be responsible, take precautions, absolutely, but it's not in itself anything more or less controversial than driving or having a barbecue.

Just because I have time, I'm going to also list my Top 5 Things that People Think are Vices but Really Aren't.

5. Selfishness. Too much is bad, obviously, but you gotta think of yourself too.

4. Drunkenness. I mean, sure, if it makes you do bad things, maybe don't get drunk. But for me, it just makes the room spin and then I pass out.

3. Laziness. As with everything else in this section, too much can hurt you and those close to you, but look at the world around you: just about every human-created bad thing you see is the result of people being too productive with their time. Relax. Have a drink. Also, there's no inherent virtue in waking up early.

2. Lust. This is related to some of the shit above. I firmly (pun intended) believe that there's a big difference between thinking something and doing it. Covet thy neighbor's spouse all you want; just know that doing something about it will almost certainly have negative consequences for everyone involved.

1. Inconsistency. Again, if you don't change when it's necessary, you're being foolish. Know when to relent and change your mind. Like I will next time one of these prompts comes up. For example, I've written before in here about how I think compassion is an important virtue. I still think it is (though it's probably the basis for fairness and acceptance). But it doesn't make my top five. Not today, anyway. Ask me again tomorrow.

9 Like • Comment • View 11 comments

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