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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:

Charity Marie - <3

about 2 hours 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

a day 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.

October 9, 2021 at 12:13am

#1018996

The Sioux Chef

Back for another "Journalistic Intentions"

[18+] entry today.

Sean Sherman

Gotta love a good pun, which is, by definition, also a bad pun. A bad pun that alliterates is even better. A bad pun combined with a quadruple alliteration (or close enough)? Gold. Sioux Chef, Sean Sherman. Come on. You gotta check out the link for that alone.

When I was in Minneapolis around the beginning of July, wandering around the riverfront in the vicinity of the waterfall and lock (once a civil engineer, always a civil engineer, and massive public works projects intrigue me), I discovered the restaurant, Owamni, featured in the above link.

Okay... "discovered" is a bad word in this context and obviously I should be shunned forever for daring to use it. It's kind of like the faux pas I made as I was checking into a hotel in Kayenta, Arizona, several years ago. Kayenta is in the Navajo nation in the far north of the state; tourists with an inexplicable need to be *shudder* outdoors use it as a gateway to all the cool shit in southern Utah, whereas I was just passing through. I'd planned the stop in advance, so I staggered into the hotel (I think it was a Holiday Inn Express, or maybe Hampton; one of those franchise chains) under my load of luggage, stumbled up to the counter, and said to the nice lady, "Yeah, hi, I have a reservation..." And immediately regretted it.

She didn't kick me out. This hotel, it turned out, included a restaurant run by a Navajo chef, and thus was I introduced, for the first time, to the absolute delight that is Navajo frybread.

The pre-invasion people living in North America were, of course, quite diverse, as is the country's climate and terrain. Without the benefit (and don't misunderstand me; it is actually a benefit) of international trade, people kind of have to use what food sources are available wherever they happen to be. This was, of course, true of people everywhere in the world, but today I'm talking specifically about the continent I live on.

But I also know this: humans are humans, wherever they are. When I was growing up, I got full-on indoctrinated into the whole "Indians lived off the land in harmony with nature" schtick. While there's probably some degree of truth in that, it's kind of idealist and dehumanizing all at the same time. Humans migrate, and we tend to take with us some of the food from wherever we came from. And as we saw several entries back, agriculture was most definitely A Thing in North America before the Europeans got here.

In any case, the point is, what the Sioux or Dakota people ate on the Northern plains would have been different from what the southern desert people ate. I mean, duh. It's kind of like how, now, you can't eat anywhere in New Mexico without being asked "red or green chili?" whereas in Minnesota, the idea of any sauce more powerful than mayonnaise is met with absolute shock and horror (yeah, yeah, I know, not all Minnesotans, whatever).

So you can imagine how thrilled I was to see the sign for Owamni there on the bank of the Mississippi, and how utterly devastated I was to find that it had not yet opened.

I think it's open now, but of course I'm not in Minnesota.

I did get to tour the river lock, though, and that was cool.

4 Like • Comment • View 5 comments

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