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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 23 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.

December 8, 2021 at 12:03am

#1022945

Transcendental

Maybe you thought you could stop thinking about "gratitude" because Thanksgiving is over.

Sunday Firesides: Graduate From the Kindergarten Class of Gratitude

I'm no stranger to knocking out strings of words on a given topic in a few minutes. Hell, I do it every night. This reads like that. Only, presumably, these authors are getting paid, and I'm not.

Is there anything more innocuous than gratitude?

Puppies, maybe?

It’s one of the few values endorsed by solemn religious leaders and vapid lifestyle gurus alike.

I'm going to start using the phrase "weaponized adjectives" to describe this sort of blatant editorializing.

Unlike other virtues, which require going against instinct (e.g., you feel afraid, but decide to act with courage anyway), with gratitude, you simply lean into it; something good happens, you feel good, and you need only recognize that warm and fuzzy sensation.

No, if something good happens, I wait for the other shoe to drop.

Yet there’s more to gratitude than commonly countenanced — higher and harder shades of it to reach for beyond its elementary-level start.

“Advanced” gratitude retains delight in someone’s admirable qualities and small acts of service . . . even after the novel and noticeable becomes the ordinary and expected.

If you say so.

If elementary gratitude is instinctual; advanced gratitude is effortful. Whereas one is merely felt, the other is expressed.

Some people say that we only appreciate the things that we have to work for. I happen to disagree. I appreciate more the things that are handed to me, because they're so hard to replace.

If, in the kindergarten class of gratitude, the warm fuzzies of thankfulness are for the heart-lightening benefit of the individual alone, in post-graduate gratitude, they are used as a spur towards being better, doing better, giving back.

And that's fine, but it doesn't go far enough.

The next level, as far as I'm concerned at least, is being grateful not just for the good things that happen, but for the shitty things.

I'll call this "transcendent" gratitude, so I can weaponize that adjective, and because that's the only thing I can think of beyond "advanced" in the limited time I have to do this entry.

Say a tree falls on your house. That sucks, right? Especially if you're in it at the time. But if you survive, transcendent gratitude is being thankful for the opportunity to step outside your comfort zone, learn new things, figure out how to make an insurance claim, navigate the emergency room for the concussion it gave you, and how to get someone to fix it as quickly as possible -- all valuable life experiences.

Or you loan a friend $5000. She doesn't pay it back. You should be grateful for that life lesson: don't lend money to friends -- or pick better friends -- or never trust her again. Or, in my case, all three.

Or your car breaks down on US 50 in Nevada, with no cell service, 110F+ temperatures, and no help within 200 miles. Be grateful for the opportunity to practice all the skills you've prepared for just such an occasion.

Now. I'm not saying I practice transcendental gratitude, at least not on a regular basis. Frankly, I'd rather give up and bitch about it. But bad shit happens, inevitably, and you can either bitch about it and give up, or be grateful for the learning experience.

And see? I can knock out a monologue about gratitude in less than a half hour, too.

3 Like • Comment • View 2 comments

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