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Sunday, Dec. 22, 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:

Annette

about 18 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 20, 2024 at 9:02am

#1078619

Revisited: "Unlucky"

Going back over 5 years, today's peek into the past takes us to an entry from July of 2019: "Unlucky"

I've written about luck several times in here, but this entry isn't directly about that; it's a play on the word "potluck." The entry is a response to a prompt, most likely from 30DBC: "What is your go-to dish to bring to a potluck? Does your family have any traditional recipes? (In Hawaii, these appetizers are called 'pupus'"

What I apparently didn't catch at the time was the reference to appetizers; in mainland North America, a potluck is when you bring a dish of any sort to a communal gathering. The dish could be an appetizer, but it could also be a main course (my entry goes on about casseroles for a good bit) or a dessert.

Casseroles, however, mystify me. I'm not sure why. They can't be that hard to do, or millions of Southern Baptists wouldn't do them, in all their various incarnations. You'd think that would teach them something about variety and the wonders of diversity, but... no. They just plop down their armies of Corningware, oblivious to the obvious metaphor.

Since then, I've tried my hand at various casseroles, with a good bit of success. They're less work than other dishes, but still harder than, say, popping a frozen thing into a microwave.

But what stumps me is that I don't know what the essential thing is that makes a casserole a casserole and not something else. Baking? You also bake lasagna; is that a casserole? Meat? Nonsense; there are plenty of vegetarian casseroles.

I've also had several entries about classification problems, like my perennial assertion that a hot dog is not a sandwich, but a taco.

So, yeah, no traditional family recipes here. Just stuff I've picked up along the road.

As I noted in that entry, if there were traditional recipes in my family, they'd be borderline inedible, and I'd have no problem letting them fade away.

Fortunately, one of the comments helped me to clarify the "what exactly makes a casserole a casserole" conundrum. I occasionally get comments here that thank me for helping the commenter learn something new, but I assure you, that works both ways.

Just lucky, I guess.

4 Like • Comment • View 3 comments

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