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Complex Numbers

by Waltz Invictus

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:

tj-Merry Mischief Maker

about 17 hours ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

about 22 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 22 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

July 23, 2024 at 9:14am

#1074310

Holy of Holies

This month's penultimate entry for "Journalistic Intentions"

[18+] takes us to the Great White North.

Montreal

A while back, a friend of mine was getting ready to visit NYC for the first time. (I promise this is relevant to the prompt.) She knows I go there fairly regularly, but every time I wanted to give her advice or suggestions, I managed to restrain myself. "I'll answer questions if she asks," I thought to myself. "It's more fun to discover things for yourself there."

And then, one day, she texted me with, "Where's the best place to get bagels?"

I immediately responded with "Montréal."

"Asshole."

There are, of course, plenty of great bagel places in New York. While I can't personally vouch for the "Montréal" answer, having never been there, I've heard it from so many different sources that I have accepted this superlative as Truth.

Which led me to wonder: How did this Francophone city in the upper reaches of North America become the Holy of Holies? (Get it, because bagels have holes? I'll be here all week.)

Obviously, it has to do with the Jewish community there. But the origins of this particular toroidal carbohydrate module stretch back, not to France, but to Poland. Like every near-perfect food, such as curry or pizza, though, they proved too popular to be limited to one country, instead spreading in their glorious roundness all over the globe.

It's true, however, that bagels entered the North American diet by way of New York, not Montréal. But they spread like cream cheese on a... well, they spread. Hell, there's even a great and popular bagel place right here in my very Southern hometown.

It's even one of the few foods that California does right. They can't make a decent pizza or pastrami sandwich, but there are at least good bagels scattered around California like poppy seeds on a... well, they're scattered.

As a side note, I once had a pastrami pizza. I was, of course, initially skeptical, but that particular abomination turned out to be quite delicious. Where was it? South freakin' Dakota, and I never would have discovered it had I not been stranded there for two days.

But I digress. We were talking about... what were we talking about? Montréal. I thought about going there before France, mostly to try the bagels. But I was concerned that I'd miss summer. There's a three-day window when the climate there would actually be comfortable for me; the problem is, one never knows exactly when those three days fall on the calendar. Usually in July, but not always.

Bagels, however, are a multi-season food. You know, many seasons. Like on an everything bagel.

4 Like • Comment

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