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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:

Aiva Raine

about 11 hours ago
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

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

January 1, 2022 at 9:14am

#1023961

Airlock.

This year's going to suck no matter what, so why not start it off with rants, courtesy of "JAFBG"

[XGC]?

As usual, I'm just tackling the prompts at random.

Unruly passenger incidents on airplanes have skyrocketed in the past couple years. What do you think about all these in-flight incidents and what should be done about it?

What the hell do you think should be done about it? We live in a world where people are slapped onto a no-fly list for jaywalking, and yet they're not banning all passengers who commit assault in a crowded flying tin can with no survivable escape routes? That is, at a minimum banning them, or for the most egregious cases, they should install airlocks in the tail cone, and anyone who smacks a flight attendant or random fellow passenger gets instantly ejected... whether the plane's still on the ground or not.

If you want to be fair about that last bit, engage the other passengers in a game of Judge, Jury and Executioner, and let them vote on it: Lifetime flight ban, fine, jail time, or airlock; you choose.

Okay, summary execution may not actually fly (pun intended, as always), but a guy can dream, right? How about this, then: Airlines slap a surcharge on everything, already. Extra legroom, checked luggage, bag of ten tiny stale pretzels, oxygen, a toilet visit, whatever. How about for a small fee -- say, $50,000 -- you're entitled to one (1) punch, slap, or kick of a flight attendant. They can still do whatever they want to you afterward, including duct-taping you to the least comfortable seat in Cattle Class, but that one smack'll cost you 50 thousand smackers. Just institute mandatory MMA training for the flight attendants so they learn to take a punch (paid for by the surcharge, of course), and we're golden.

Or, you know, if they're really serious about not wanting passengers to get all unruly and shit, how about not packing us in like sardines? Sure, that'll increase the cost of a plane ticket, thus causing fewer people to fly, but are you concerned about the environment, or not?

Since that's not going to happen, free and mandatory Valium for adult passengers might work, too. Well, not free, obviously, but tack it on as another surcharge because they love doing that. It would be especially fun for us drunks. I was given Valium for (I think) the first time in my life last month, to keep me from screaming in terror as they fucked with my eyeballs, and it worked. Didn't drink afterwards, though.

Vaporized THC in the cabin air is an option as well. No better time to get high than when you're getting high, and stoners don't get violent unless they're also mean drunks or someone laced their weed with PCP or some shit like that.

Speaking of which, I'll also tell you one thing that should not be done about it, but apparently has been, and that's banning drinking or bar services on flights. Shit, alcohol is the only thing that makes cramming into steerage remotely tolerable, and most of us drunks aren't mean drunks; as with everything, the few who are ruin it for everyone else. Or, rather, the pissant airline companies use that excuse to ruin it for everyone else. It's not the poor alcohol's fault; the blame lies squarely on the shoulders of the offending person themself.

In any case, this hardly affects me because I don't fly much these days, for obvious reasons. Sure, there was the Delta flight I took in July when I was stranded in South fracking Dakota, but that was a legitimate emergency. No one got punched, all the flights were on time or early, and no one bitched about having to wear a mask on the completely full planes.

7 Like • Comment • View 4 comments

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