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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:

🌕 HuntersMoon

about 9 hours ago
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

a day ago
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

🌕 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

April 13, 2022 at 12:02am

#1030623

Zoned Out

An entry for "Journalistic Intentions"

[18+]...

Gulf of Mexico Dead Zone

From what I've heard, the Earth looked a little different 65 million years ago.

Here's a drawing: https://images.slideplayer.com/16/5101171/slides/slide_2.jpg

Some of the continents are vaguely recognizable. You can make out South America, Africa, Australia as it was divorcing from Antarctica. In between Africa and Australia, just east of what is already recognizable as Madagascar? That'll become India in several million years as it migrates north and forms the Himalayas.

And that big explosion-looking thing in red? In what's going to become the Gulf of Mexico? That's the impact crater that they say probably killed off most of the dinosaurs.

Though they're still speculating about that, last I heard, it remains the most likely scenario. Whatever the actual cause, there's little doubt that it was around that time when the non-avian dinosaurs died off, paving the way for mammals to take over, which eventually led to the evolution of some clever apes who, in the span of about 100 years, wiped out a lot of the deposits of crude oil that it took billions of years for nature to sequester underground.

What is certain is that the impact would have killed off anything in its immediate vicinity. The rest was, so the speculation goes, devastated by the resulting sudden change in climate.

It's a myth that crude oil is dead dinosaurs. A myth, but a persistent one. Sinclair still uses a dinosaur for its logo, which was originally a brontosaurus, then an apatosaurus, and now they're saying no, wait, it's actually a brontosaurus after all.

No, the bulk of these deposits were formed long before the dinosaurs. Had they developed oil wells, perhaps they would have sucked the planet dry before we even showed up on the stage. But they didn't, so it waited another 65 million years or so until we came along and decided we needed energy.

And one of the places we get that energy from happens to be the Gulf of Mexico. We all know about the massive oil spill there from over a decade ago, but that wasn't the only one. These spills killed a bunch of shit and drove the rest off.

Another Gulf of Mexico dead zone. Not from a sudden impact, but in geological time, 100 years might as well be a minute.

People can't help but speculate: what comes after humans, after we've experienced the inevitable extinction event? Will another civilization arise? Maybe cockroaches will learn to build and drive cars?

Well, no. Because we've sucked all the oil out that powered those cars. And taken away all the low-hanging fruit -- the once-easy-to-find minerals that kick-started each of what we like to call "ages:" stone, bronze, iron, nuclear, whatever. It will take millions, even billions, of years to recover those, if it happens at all, as continents continue to drift and new material gets sucked up from the mantle.

No, if another species on earth ever managed to learn to make tools and use them to fight each other over other resources -- they couldn't, because there's nothing left on the surface, not enough to make a difference, anyway.

The Earth will recover, as it did from the mass extinction that ended the Cretaceous. Life will, uh, find a way, to paraphrase Jurassic Park. But that's it for what we like to call "civilization."

I can't say the planet will be worse off for it. Sucks for us, though.

5 Like • Comment • View 3 comments

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