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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:

Annette

about 7 hours ago
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 ✍️

a day ago
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

a day ago
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

🌕 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

September 21, 2020 at 12:05am

#993819

Out Of Control

What, me worry?

PROMPT September 21st

One thing outside of my control that I need to stop worrying about is...

I'm... not really the worrying type.

As the prompt suggests, there are things in my control and things that aren't. If a situation is, at least in part, in my control, then I tend to do something about it. If it's not, then I figure out a way to deal with it -- usually by imagining the worst possible outcome, mentally preparing for that, and then being relieved when it turns out to be not as bad as I expected.

Of course, like everyone else, I have certain concerns. No point worrying about them, though. It's a waste of brain power, when that brain power could be used to play video games or get distracted with booze.

I'm sure there are a lot of things on everyone's mind right now: pandemic, economic struggles, upcoming election in the US, social issues, the impending end of Western civilization, and all the other joy that 2020 has brought us. Hell, I was just reading where archaeologists found a bunch of sarcophagi

in Egypt. I mean, I'm a rational guy, but unearthing cursed mummies in 2020 sounds like a Really Bad Idea, and these archaeologists probably should have watched more horror movies before proceeding.

Point is, there's not a damn thing I can do, and if there were, I'd be doing it instead of turning it over and over in my mind. It's not like I can fly to Egypt and ask the archaeologists what the hell they were thinking, and even if I could, it wouldn't do any good.

In case it's not obvious, I'm joking about the mummy curse thing; it's a worn-out horror trope, which makes it ripe for comedy. Jokes are what keep me from worrying. I haven't found many situations yet that I couldn't joke about. Hell, I was getting treated for a heart attack, watching my ticker beat on the screen, millimeters away from possible death, and all I could say was, "Huh... it's not made of stone after all."

If you can't control the situation -- and much of the time, you can't -- you can control your response to it. I recognize that worry is one of those emotions that's really hard to address, but just because I can't control something doesn't mean I'm going to let it control me.

Usually, though, it's not about control, but about just letting go. I don't accept that everything's in some higher being's hands, or has a purpose. Also, there's no telling what the future will bring; could a situation come up where I do start to worry? It's possible. It's just not happening right now, and I'm certainly not going to worry about getting worried.

9 Like • Comment • View 12 comments

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