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Saturday, Dec. 21, 2024

6:59am EST

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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 13 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 18 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 18 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

a day ago
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

September 11, 2024 at 11:48am

#1076615

Drop and Gimme Twenty

Somewhat predictably, I'll take a break from the usual today in order to blab about this being my 20-year anniversary here.

Unfortunately, I said most of what I wanted to say back on September 1, as we began the site's 24th anniversary: "Four and Twenty"

Having my own milestone so soon after that of the website itself, though, is kind of like I'd imagine it would feel like for your birthday to be on December 26: everyone's burned out on celebrating, including me. Especially me.

Which is fine. I'm on board with celebrating actual birthdays, but membership anniversaries are just, well, whatever. Still, this being the 20th, one of those nice rounded-end numbers, I felt I should say something about it.

Things were a bit different back in 2004. Smartphones weren't ubiquitous yet. The internet hadn't become a mire of scams, ads, and influenzas. And a certain other event that took place on a September 11 was still fresh on everyone's mind.

I hadn't intended to join on the 11th, for that reason. I tried to create an account here the previous day (my dad's birthday, and he was still alive back then, so already a significant day for me), but for whatever technical reason, it never took. That's also how my username got the annoying 02 at the end; while the account didn't work, my attempt was enough to block off just "cathartes" as already in use. It's been long enough that I don't remember all the details exactly (hell, 20 days is probably long enough for that, for me), but I vaguely recall creating this account with help from a friend who was already a member, shortly after midnight, forcing my account anniversary to be on a day that was already infamous.

I've considered changing my username to something else, but never went through with it. It's kind of part of my identity now, so I'm ambivalent about the idea.

So, I'll just finish by posting what I'm pretty sure was my first item on here, created on September 11, 2004—but which I'd written some years earlier: "Ghost Poem #1"

[ASR]

Odd that it was a poem, I suppose, because I'm more of a fiction writer and, now, a blogger, but I suppose it was something quick and simple to put up here to get started. And even back then, when I had an actual job and a spouse, I was all about quick and simple.

Some things don't change all that much.

6 Like • Comment • View 4 comments

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