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Friday, May. 17, 2024

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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 19, 2020 at 12:01am

#996208

Juxtaposition

Entry #8 of 8 in

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts February 1!
#2213121 by Elisa the Bunny Stik

hairtherapy@gilbertneurolgy.com

There exists an animal called the Japanese Dwarf Flying Squirrel.

Each word in its English name has a specific meaning:

Japanese: from Japan
Dwarf: smaller than usual
Flying: able to soar
Squirrel: Cute rodent with bushy-ass tail

Nothing really special about any of these individual words. Quite common, actually. We see examples of most of them every day, either in our backyards or on the internet. Well, maybe I see more Japanese than others because... well, just you never mind.

The point is, put those words together and you get Epic Awesomeness. A Japanese Dwarf Flying Squirrel. Seriously, go to that link above and look at it. LOOK AT IT. And look at this picture,

too.

If that is not one of the cutest, if not THE cutest, thing you have ever seen, there is something seriously wrong with you. Possibly even a neurological disorder.

Perhaps, then, you need hair therapy.

See, unlike four words forming a unique synergy, as with the squirrel, sometimes you get four words that make you go... "Huh?"

Hair - humans' answer to fur; some have more than others
Therapy - a process to help restore a person's mind or body
Gilbert - somebody's name, presumably
Neurology - the study of the brain and nervous system

Each one of those words, taken individually, is rather innocuous -- though my personal connotation of neurology stems from when they took out part of my ex-wife's brain.

Taken together, though, they make no sense, not even a little.

I am, however, reminded of the hairshirt that penitents supposedly wore, and perhaps still do. Something deliberately uncomfortable that focuses the mind, hopefully forcing one to contemplate the numinous and esoteric rather than the pleasures of the flesh.

As a dedicated hedonist, though, I prefer cotton or silk. Just not squirrel fur. That would be cruel.

Mini-Contest Results!

I appreciate all the comments, but only one seemed to address the question in my last entry. So today's Merit Badge will go to WakeUpAndLive️~🚬🚭2024

for:

Scientists discovered how to control a biomechanical hand, just by thoughts- 2009

Amputee Pierpaolo Petruzziello learned to control a biomechanical hand connected to his arm nerves with just wires and electrodes and became the first person to make movements like finger wiggling, making a fist, and grabbing objects using just his thoughts.

Which is truly cool (and, serendipitiously, ties in to the "neurology" thing in this entry, which was chosen at random). However, can you imagine what would happen if someone figured out a way to hack it?

"Why are you punching yourself?"

5 Like • Comment • View 5 comments

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