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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:

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
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

May 3, 2024 at 11:58am
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

October 19, 2018 at 12:50am

#943731

First Man

I went to see First Man today, that movie about Neil Armstrong and the space race.

Saw it at Alamo, of course, the theater with the beer taps, so I was able to get good and buzzed first. (See what I did there? I'm way too proud of that one.)

Spoiler alert: They land on the Moon.

I should note that Ryan Gosling really bugs the hell out of me. I don't know why. Maybe it's because he was in Blade Runner 2040. He looks like someone who gets his lunch money extorted on a daily basis.

Still, I think he nailed this one.

Okay, look, I'm just going to say it, even though I've said it before: I think the moon landing is not only the most significant achievement in human history, it's the most significant achievement that can ever be in human history. It's the moment that we first set boots on another world, satisfying the human desire for exploration and horizon expansion. Hopefully there will be more such moments, but that was the first. Yes, the discovery of extraterrestrial life (as per my last entry) will probably be the greatest discovery, but I'm making a distinction between achievements and discoveries.

That's arguable, I know. But it's why I went to see the movie. It didn't disappoint on that front.

It irks me that no one seems to be able to talk about the movie, or the events it depicts, without someone bringing up the "moon landing hoax" nonsense. (In this case, it's me bringing it up; it still irks me.) I'm not sure I've ever been able to articulate exactly what it is about that garbage that pisses me off so thoroughly, but I think the movie helped me figure it out - mostly because it focused on the human elements involved.

Using little more than a slide rule and a straightedge, we sent dudes to the moon in a rocket with the name of a god of the land on a mission named for the god of the sun. But these names were symbolic - this was a purely, epically human adventure. No gods transported us to another world. No demons, no monsters chased us into the heavens. No angels, no devils; only people.

And that's what bugs me about these conspiracy nuts. They offend me on a basic, visceral level. To deny this achievement is to deny humanity itself, to condemn us forever to mediocrity. It's as if to say, "Look at Earth. Look how we can't get anything right. It's impossible to believe that we can ever achieve greatness; therefore, we didn't, but we could fake it." It's the same sort of contempt for our potential that leads people to believe that aliens built the Pyramids, or fairies built Stonehenge. Because sometimes skyscrapers crumble and bridges buckle, because we still bicker among ourselves and kill and enslave, because we pollute the oceans with plastic and poke holes in the ozone layer, obviously we can't do anything right, according to these loudmouths.

But we contradict ourselves. We are large; we contain multitudes. We are destroyers and creators alike. We are thieves and we are philanthropists. We can bring darkness, and we can bring light.

We are the monsters, and we are the gods.

2 Like • Comment • View 2 comments

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