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Tuesday, Dec. 31, 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

a day ago
In response to "Revisited: "None More Black""

Favorite color? Growing up it was deep red, but having a little brother, his favorite color also had to be red, so I decided to pick blue. His also turned blue, so I decided not to have a favorite, but to like all colors. But, what do you get if you mix together all the colors? Black.

Waltz Invictus

a day ago
In response to "Revisited: "None More Black""

🌖 HuntersMoon

: See also my many polemics on the fruit status of tomatoes.

1 Like

🌖 HuntersMoon

a day ago
In response to "Revisited: "None More Black""

Knowing your penchant for "scientific" foundations for answers, black is not a color.

Black's status as a color varies depending on the perspective:

Scientific perspective: Black is not a color; it is the absence or complete absorption of visible light, making it an achromatic shade.
Artistic perspective: In art and design, black is treated as a color because it can be created by combining pigments and provides contrast.
Human perception: Black evokes feelings similar to other colors and is often associated with darkness, power, and elegance.

2 Like

tj-Merry Mischief Maker

Dec 28, 2024 at 3:23pm
In response to "Extro Special"

I'll also use the spelling extrovert because if I use extravert my spell checker flags it. In college psychology our professor termed his own words, innervert and outervert because he thought they fit better. I, however, thought they sounded like definitions of belly buttons.

1 Like

Kåre เลียม Enga

Dec 28, 2024 at 9:11am
In response to "Extro Special"

I probably fit omnivert best. I'm temperamental.

Words change... definitions change... we change.

1 Like

tj-Merry Mischief Maker

Dec 27, 2024 at 3:41pm
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

Dec 27, 2024 at 10:33am
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

Dec 27, 2024 at 8:43am
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

Dec 26, 2024 at 4:20pm
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

Dec 26, 2024 at 1:07pm
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

September 25, 2024 at 1:42pm

#1077271

There Is A Such Thing As Coincidence

Yesterday's adventure took me on the TGV from Paris to Tours.

Don't ask me what the letters stand for. You can look it up same as I could, but I don't really want to know. Far as I'm concerned, they stand for Train Go Vwhooosh!

Out of curiosity, while on the train, I checked a website that used GPS data to determine one's current speed. Now, obviously, French high-speed rail can only move in km/h, and I can convert just fine in my head, but having spent most of my life moving at mph, I clocked in at 180-190mph.

Upon arrival in Tours, I made the questionable decision to walk to my hotel. Google said it was mostly flat, and it didn't lie. What it didn't tell me was that it was also mostly tiled sidewalks. Try rolling two suitcases on tiled sidewalks for 1600 meters.

The travel agent had some suggestions for what to do in Tours for the rest of the afternoon, and they were good suggestions, involving historic neighborhoods and buildings. I like that sort of thing well enough, but I have my priorities, so I set out to find beer.

What I found was very good beer, and a couple of hours later, I staggered back to the hotel, only to find, upon logging in to WDC, that our very own Annette

was, by cosmic coincidence, also in Tours at that moment.

So of course I had to stagger all the way to where she was staying which was, comically, right next to the train station.

At least I wasn't dragging luggage, this time.

Now, look, I don't just go knocking on random peoples' doors, even if they are regulars here on Writing.com. But I'd spent a week in the L.A. area a while back, being shepherded around by Annette and her husband. So it's not like we didn't know each other. I didn't knock on her door, either; we met in the lobby and went to have drinks. Soft drinks, because even I have my limits.

I got back to the hotel just after midnight, which probably wasn't the best idea, either; I had to get up at some ungodly cow-milking hour this morning to go on a planned-and-paid-for tour of some of the catwaters in the area. Catwaters? Wait, no, I mean chateaux. (The best part about learning another language is gaining the ability to make horrible puns in both languages.) But that's a discussion for tomorrow.

Pic posted with permission:

8 Like • Comment • View 4 comments

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