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Saturday, Dec. 21, 2024

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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 13, 2024 at 10:34am

#1073898

Surprise Me

A brief travel planning update:

I met with the travel agent on Wednesday. As a reminder, I'm using a travel agent this time because a) I'm entirely too lazy to coordinate my own itinerary; b) I don't know exactly what I want; and c) I've never done it before, so it'll be a new experience for me.

I told her basically what I wanted to do (wine and beer tourism in France and Belgium), so she suggested three locations in France: Loire, Burgundy, and Paris.

"So you'll fly into Paris and spend... how long there? Five days?" (I'd told her maybe three weeks for the entire trip.)

I'm like, "I'm not exceptionally interested in Paris. The city is dirty, and the people are rude and will be tired of foreign tourists after the Olympics."

I mean, I get flying into Paris. There's a big international airport there, and the other places I want to visit are generally in the northern part of the country. But thinking I want to spend time there is a big assumption.

Then I remembered that I'd heard the Paris craft beer scene had developed nicely in the past few years. Plus, she dangled "reservations at a Michelin-starred restaurant" in my hungry face. (I think they make most of their money from kickbacks, which is fine.) So okay, sure, Paris. Just not a lot of the touristy places. And maybe three days, not five. I know it's an enormous city and you can spend years there without running out of new things to do, but I'd rather focus on other locations.

The rest of the trip is countryside and small towns. Well, mostly. Nothing's detailed yet, but Belgium might involve staying in Brussels, for which I don't have any objection.

The problem with France, I've found, is that there's pretty much nowhere in the entire country that I don't want to spend time in. Well, maybe some of the freezing cold snow-peaked mountain parts. I wouldn't mind visiting them briefly, or seeing them from a warm, comfortable distance, but, as with every other high mountain range, the combination of colder temperatures and lack of air pressure is anathema to me. Plus, I might be expected to "ski," or "hike," or do any number of disgusting outdoor activities.

Yes, I've done it, like when I spent a week at a science camp in the Colorado Rockies. That's how I know it's not for me.

So, now I'm waiting for them to stitch together a draft of a travel plan. I'll get to look at it and change things if I want. I told her, "Don't worry; I like surprises... but only if they're pleasant ones."

She didn't find that nearly as amusing as I did.

5 Like • Comment • View 3 comments

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