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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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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

January 2, 2019 at 1:02am

#948671

Mas Tequila!

I have mixed feelings about birthdays.

Mine is in February. As I've noted before, February is my most hated month. Even though the days are getting noticeably longer then, it's still cold, and it contains the most hated day of all: Valentine's Day.

Fortunately, my birthday is after that dreaded occasion, so there's less of that creepy blood-red decoration everywhere. Instead, stores start lining up for Easter. I'm no fan of pastels, either, but anything's better than crimson.

After celebrating as many birthdays as I have, they all start to blend together. I know most of my adult birthdays have involved tequila. That's kind of an unintended tradition for me.

It started on my 21st birthday. That is, for you foreigners, the first day one can legally purchase or drink tequila (or any other booze) in this benighted country. Now, at the time, I'd already been legally drinking beer and wine for two years. It was, as I recall, on my 19th birthday that my state passed a law raising the drinking age to 21 for everything (it didn't take effect until that June, and I was grandfathered in, anyway). Stupid fucking law - get 'em used to alcohol early, is what I say. It becomes less of a Thing that way, and you get less abuse later.

But, in my neverending quest for alcohol positivity, I digress. The tradition, as dictated by my college housemates at the time, was to quaff 21 shots of tequila on one's 21st birthday. Now that... that's not something I'd recommend to anyone who hasn't practiced, and legally, you haven't practiced by then. Legally. Ahem. The problem was, though the bottle was labeled "tequila," and it was, by the laws of both Mexico and the US, tequila, it wasn't tequila; it was Cuervo Gold.

See, to be tequila, it has to a) be at least 51% from agave and b) be manufactured in a particular region of Mexico. Anything with 51%+ agave made outside that area has to be called something else, usually mezcal (that's the one with the worm). Anything with less than 51% agave has to be called something else too, usually "disgusting rotgut that'll kill you." So Cuervo, attempting to make the cheapest shit possible that can still be called tequila, fills up the other 49% with Quetzalcoatl-knows-what, and adds caramel color to make it look somewhat like it's been aged in barrels the way the unpronounceable gods intended.

Dammit, I'm digressing again. What I mean to say is, while that incident put me understandably off tequila for several years, I love real tequila, the stuff made from 100% agave. It comes in four basic varieties: Blanco, which is unaged; Reposado, which is aged a little bit; Anejo, which is aged at least 1 year, and Extra Anejo, which is aged 3+ years.

DAMMIT.

Birthdays.

Right. I'm getting there.

Ever since I discovered real tequila, which was significantly after my 21st birthday, it's been an important part of my birthday celebration. In margaritas. In shots from a ski along with friends while I was on the island of St. Thomas. (You heard right. A snow ski. On a tropical island. In February. Using Mexican liquor.) A flight of really good, really expensive Anejo tequilas in a local bar. A flight of not so expensive tequilas in a bar in Vegas.

So, as you can imagine, all those birthdays kind of blend together.

Therefore, none of them can be considered my most memorable birthday. That would be the one that didn't involve tequila and, instead, involved an IV drip in a hospital bed while recovering from the heart attack and resulting surgery I enjoyed on the evening before my birthday.

Memorable, yes. But it sucked. And you can bet that as soon as I got out, there was only one thing I wanted, and fortunately, there's a tequila bar just a few blocks from the hospital.

I mean, why mess with tradition?

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