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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:

Annette

about 11 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

June 11, 2024 at 1:26pm

#1072479

No Cornea Jokes Today

One of the immeasurable joys of getting older is we get to go visit doctors and other medical professionals more often. For instance, me, this morning, so this is going to be a fairly brief personal update rather than deep philosophical musings about whether Chicago pizza is actually pizza (it's not) or scorn at the sorry state of science reporting.

Some long-time readers might remember that back in the dark ages of 2021, I had cataract surgery in both eyes. Today's visit to the eye doctor served as a general check-up and 2.5-year follow-up to that.

Now, I know I like to kvetch, whinge, moan, and complain in here. But this time, I have nothing to complain about. Everything, according to the eye doctor (don't make me spell optha-whatever), is fine. Sure, my vision is slightly worse than it was 30 years ago, but it's a lot better than it was 5 years ago.

What I mostly wanted to share, though, was that the doc, who I go to both because she's very thorough and because she's married to a former colleague of mine, is a massive nerd. I mean, you expect that from science-oriented professions, but she keeps up with the latest ocular-testing gadgets, and this time, she had a new toy: a virtual reality headset programmed to do part of the eye exam.

You put on the headset, and a little blue floating cartoon lady (you can tell the gender from the voice and the ponytail; I have a ponytail sometimes, too, but my voice and goatee give away the game) walks you through an exercise where they measure your visual focus distance. This involves staring at a target while a light show goes on all around you like you're moving through space in a game.

Turns out my focus isn't quite right, but not off enough to cause serious eye problems or require glasses. Which is still weird to me, not needing glasses for anything at my age. Well, sunglasses for protection from the harsh glare of the accursed daystar, sure, but not prescription ones, and I've always needed shades.

And the only reason why?

Science.

I'd be effectively blind right now without science. Well, not really; without science, I'd have died before I could go blind.

So if you ever wonder why I bang on about nerd stuff in here a lot... well, that's one reason why.

4 Like • Comment • View 1 comment

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