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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

about 19 hours 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

a day 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

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
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

Dec 19, 2024 at 3:43pm
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

October 4, 2024 at 1:59am

#1077735

Coats Do What Now?

For my final full day in France, I took a small-group tour to the wine region of the Côtes du Rhône.

In contrast with the previous day's trips, I wasn't very familiar with the Côtes du Rhône vintages. This, of course, is why I went. I find that, when traveling, some mixture of the familiar and the new is ideal, though I expect the proportions would differ for everyone.

While I don't think I'd ever had a wine from this region before, some of the grapes they're based on are fairly popular to grow in the US.

The tour group itself was pretty interesting. Some of us ugly Americans, a couple from Quebec, and three people from Australia, who, while initially distrustful of my Americanity, quickly warmed up when I assured them (out of earshot of the tour guide) that I very much enjoy Australian Shiraz. While the guide insisted that Syrah, one of the grapes in Côtes du Rhône, is not the same thing as Shiraz, it totally is; it's just grown on very nearly the exact opposite side of the world.

The tour guide himself, who looked a bit like Kiefer Sutherland, was otherwise very knowledgeable, and spoke good enough English that all of us varied Anglophones mostly understood him.

The problem comes in when some unknown place name, or grape name, pops up in spoken French.

Like, if someone comes up to me and says "Bonjour, peux-je vous aider?" I can work out what they're saying. But if I'm at a wine tasting, even if it's mostly in English, it might go something like this:

"This wine comes from the pl***du*** region, near B***on and the S**** river valley. If you visit there, be sure to go to D****de*****, a fine restaurant that serves bl*****, v*******de la *******tion, and many very good wines, including Petit ********tre, Vo******** Blanc, and sparkling Dr*******"

It's tiring, to be honest. I started asking for spellings. To make things worse, my hearing isn't that great thanks to 50 years of rock concerts (no regrets), and I'm not asking you to repeat yourself because I don't understand French; I'm asking you to repeat yourself because I literally can't hear you over the ambient mumbles.

Ah, well, soon I get to complain about the same thing in Dutch (or at least the version of it known as Flemish; I don't know the details there), as I'm leaving for Bruges today. It's a tight schedule: catch a train to Brussels, transfer to a train to Bruges, get to the hotel from there somehow (Uber seems to be wonky in Belgium; apparently, only taxi drivers can do Uber, thus defeating the whole purpose but providing job security), then find a certain statue in a city saturated with statues to meet a beer guide who will take me... well, I don't care, as long as there's Belgian beer.

I'll wrap up with another landscape picture, this one of the Rhône Valley.

6 Like • Comment • View 2 comments

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