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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 27, 2018 at 12:32am

#944263

Fear Itself

With Halloween coming up, I got to thinking today: What would truly frighten me?

Partly, this is because of a Cracked article that covers a topic I've been talking about:

http://www.cracked.com/personal-experiences-2580-6-reasons-sleep-paralysis-most-...

(Cracked used to be better. Now they mostly suck, but they do occasionally have decent articles.)

While sleep paralysis is certainly terrifying at the time it happens, I don't lie awake at night dreading it, it barely affects the rest of my life, and I wouldn't call it the scariest thing that's ever happened to me. But when thinking about what the scariest thing that's ever happened to me might be, my brain draws blanks. Possibly this is out of self-preservation - I don't want to remember something that scared the living shit out of me (note: I've never been frightened to that literal degree).

Some people are afraid of spiders or snakes. Spiders, snakes, large insects, wasps, and so on certainly startle me, but once I get over the initial WTF, they're all actually pretty cool. Not that I'd want to pet them or anything, but they're fascinating.

Or take the clown phobia thing. For some people, coulrophobia is a real thing. I like to joke about it, not as a way of facing my (nonexistent) fear of clowns, but just because it's inherently funny. I probably shouldn't joke about it because it's mean, but hey, I am what I am. I even spent a night in the infamous, haunted Clown Motel in Tonopah, Nevada

once, and the only scary part of that was that it was 17 degrees F outside and it took me an hour to figure out how to make the room heater work.

I'm not afraid of death. I've been too close to it too many times to fear it. I'm certainly not excited about the prospect, but it's inevitable, so I don't worry about it. I'm kinda terrified of dementia, though; both my parents died from it after long, slow declines and I do not want to go through that or put my friends through it (not a genetic issue; they were my adoptive parents).

And now I have to face a harsh truth: even if I did know what I was most scared of, I'd be reluctant to write it down or tell anyone about it. Not because writing would make it so; that's superstitious hogwash. But people suck, and someone would find a way to use it against me. Like if I said "there is nothing in the world I fear more than ducks," I'd get spammed with Geico ads.

(Ducks are awesome, by the way. Also inherently funny. I've said before that if you're not sure how to make something funny, just throw in a duck.)

So I guess this entry is going to end unresolved. You don't get to know my biggest fear. On the other hand, I'm not sure what it could be, either.

1 Like • Comment • View 1 comment

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