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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 31, 2018 at 12:22am

#944571

Atlantic City

I love depressing music.

To paraphrase the Doctor Who episode "Blink," "What's wrong with sad? It's happy for deep people."

I'm probably not all that deep, though. The things I like, they're mostly all right there on the surface: good food, good drink, money, movies, music, and video games. I'm no philosopher; I don't even have a liberal arts education, having opted instead for a very practical engineering degree.

And yet, when I hear a sad song, it makes me happy. I don't know why. I did notice on my first cross-country trip, years ago now, that my playlist is probably 75% songs about travel, the road, or cars. This has been true even before I spent days gripping a steering wheel, blinking into the setting sun, alone with my music and my thoughts.

But a good 90% of my favorite songs are what some people call "depressing" and I call "awesome." But hey, you already knew I was a Springsteen fan.

So like I said last time, I had to take an emergency trip to Atlantic City to hang out with an old friend who's going through a divorce. He needed it. I'd just as soon never go there again. See, I've been to all the classic gambling hotspots in the US: Las Vegas, Reno, and Atlantic City. Vegas is all about overdoing everything; it's exuberant and bright and it's like that rich friend you have, or would like to have, who laughs at everything, drives a Ferrari, and flashes a Rolex. Reno is... depressing. And not in a good way, not like the Tom Waits or Johnny Cash songs about the place. One time, driving through Reno, I spotted a billboard advertising a Morrissey concert. That's right; Reno is so depressing that they had to bring in Morrissey to cheer it up.

Atlantic City makes Reno look like Disney World.

Used to be, AC was the only place on the East Coast to gamble, so people went there from all over. Lately, though, Delaware, Maryland, Pennsylvania, West Virginia, Connecticut and even bloody New York have legalized gambling to some degree or another, which leaves Atlantic City with very little reason to exist beyond sheer inertia and classic Jersey stubbornness.

But they still have bars, and blackjack, and usually you can avoid the scam artists wandering in off the streets for long enough to let casino security kick them out. And, unlike Vegas or Reno, if you look out the window you can sometimes see the ocean, and forget for a moment that those waves will one day drown the city in a flood of sharks and used needles.

Sometimes the only purpose of a place is to remind you of how good you actually have it. Or - maybe - substitute "song" for "place" and now I might begin to understand my taste in music.

Everything dies, baby, that's a fact
But maybe everything that dies someday comes back.

2 Like • Comment • View 2 comments

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