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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:

Annette

20 minutes ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

about 18 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 23 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 23 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

September 28, 2024 at 2:17am

#1077370

To the East

Most of yesterday was taken up by traveling. To get from Tours to Dijon, apparently there's no direct way, or at least not one that gave kickbacks to my travel agent. So it started with me taking an Uber from my hotel to the Tours train station, because now I know better than to roll luggage for that mile. Then the TGV back to Paris, during which, for some reason I absolutely cannot comprehend, my assigned seat was right next to someone else... while there were maybe 2 other people in the entire car.

But the real fun was when I got back to Paris and met the chauffeur for the ride from Gare Montparnasse across the Seine to Gare de l'Est, which is the station with the train to Dijon. The chauffeur didn't speak very good English or French, but he spoke excellent Ukrainian. At least I assume he did; I know almost nothing about that language. But he was very good at pointing out the Paris sights along the way, in some version of English with a Ukrainian accent.

"There is Tour Eiffel. And this building on left?" He indicated one with scaffolding. "Ukrainian mob has construction contract." We drove a bit further. "There on right is Notre Dame. And over there, building by Ukrainian mob." I wanted to ask him if the mob also did the Notre Dame reconstruction, but I knew better. He pointed out other important Ukrainian construction jobs along the way, too.

Now, look. It's entirely possible that "mob" was a bad translation of something else in Ukrainian. Something innocuous like "Fine Upstanding Ukrainian Construction And Renovation Company And Not Mob At All We Promise And Pinky Swear." But I choose to believe that my chauffeur, who was about my age, was an actual member of the actual Ukrainian mob and did the chauffeur thing as a day gig.

Just in case, I gave him an enormous gratuity.

As Skinny Pete said in The Italian Job, "If there's one thing I know, it's never to mess with mother nature, mother-in-laws, and mother-freaking Ukrainians."

After that, the train (the slow kind) to Dijon was a letdown. Hell, the rest of the trip might well be a letdown.

Things picked up again, though, once in Mustard City. The hotel, this time, is like 100 meters from the station. It has a lovely little bar. I had dinner elsewhere, but came back for the bar, where I got acquainted, for the first time, with a regional (the east of France) custom: Picon bière.

Mostly, they drink Belgians here, because, as I've said numerous times, traditional French beer is ass (also, it's wine country). But apparently, it's not flavorful enough for them (QUOI?!) so they add a shot of a kind of orange bitters called, you guessed it, Picon.

And whaddayaknow, it's actually a pretty good combination. Sadly, Picon isn't generally available in the US, so I'll have to enjoy it while I'm here and then smugly brag about it every time I drink a Belgian beer back home.

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