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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

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Annette

about 9 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 14, 2019 at 12:10am

#966151

Vulture

PROMPT September 14th

Today’s prompt was written by Prosperous Snow celebrating

!

It's said that beauty is in the eye of the beholder. Describe something that you think is beautiful or attractive that someone else might consider unattractive or ugly.

Your mom.

Okay, but really, yes, beauty is highly subjective, and it's not always about physical appearance.

I'll choose my favorite example: the turkey vulture

.

Those birds are, I think the vast majority of people would agree, amazingly unattractive. Ugly, even. So it's not their appearance that is appealing, or even their feeding habits - the idea of eating carrion is repulsive by any human standards.

That's why they're bald, you know. So they can stick their heads deep into a corpse without fouling head feathers. Well, the mechanics of evolution are more complex than that, but that's the general outcome of natural selection in vultures.

And yet, we humans eat carrion, also. Not, to be sure, rotting corpses; but everything we eat (yes, even if you're vegan) is dead. Fresher than a vulture's meal, perhaps, but still... dead. I mean, it's not like lions or whatever eat prey while it's still alive, but there's a brief window there between "I killed it" and "leave it for the vultures," and that window is longer for us, because we have the technology to make it so.

But that brings us to the true beauty of vultures: they remove from the environment those things that, were they to be left to rot, could easily spread sickness. They're the sanitation engineers of the animal kingdom, thus inspiring the scientific name of the turkey vulture: cathartes aura, "golden purifier." They do the job no one else will - or even can - do, and are reviled for it.

It doesn't stop there, though. Turkey vultures in particular are remarkably efficient birds. They won't even flap their wings if they don't have to, preferring instead to locate convenient updrafts and glide to higher vantage points. Maximum reward for minimum effort: I respect, admire, and emulate that. And it seems they don't fly because they have to, but because they want to. I mean, wouldn't you?

There's a popular misconception that vultures circle around animals who are near death, waiting for that moment when they can get their meal. This is not the case. First of all, no self-respecting vulture is going to start munching on a dead beast while it's still fresh enough for apex predators to get their bites in, not unless they're really hungry. Second, the circling is actually the birds staying in an updraft. Hang glider pilots like to look for vultures so they can tell where the thermals are.

They're not cute. They're not cuddly. They're not threats. They're not pets. But they are, in their own way, beautiful.

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