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Tuesday, Dec. 31, 2024

1:24am 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

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

June 25, 2024 at 7:57am

#1073156

Can't Spell Success without Sucs

Okay. Fine. Sometimes, clickbait works on me. It draws me in, fuels my outrage, makes me want to read more so I can rant about it..

Richard Branson says money isn't a good way to measure success: Focus on this 1 word instead, it's 'all that really matters'

Which is exactly the kind of thing I would say if I were a billionaire and the poors kept grumbling about dragging me and my head to a guillotine. It's like when they try to convince us that "money can't buy happiness" while they're flying in their private jets, smiling and sipping a gin and tonic made with low-paid laborer tears.

But let's hear this rich guy's take on it, anyway.

Richard Branson doesn't want to be defined by his money.

Well, you could give it all away and see how you're defined then. (Preferably, to me.)

"Maybe in America, 'billionaire' is a sign of success, but that rankles me," says Branson. "I think that your reputation is what you create."

Didn't his company declare bankruptcy recently? Oh, yeah, one of them did, last year.

Such success.

The company is largely responsible for his estimated net worth of $2.5 billion, according to Forbes — but he chafes at the idea he created it to make money.

Bet he wouldn't have done it if he didn't think it'd be profitable, though.

In fairness, $2.5 billion is small potatoes compared to people like Bezos or Musk, both of whom I mention because they're his direct competitors in the spaceflight field.

Of course, success is never guaranteed. If you do follow your passions, you'll still need factors like talent and perseverance on your side to avoid falling flat, experts say.

Mostly, though, you need luck.

And the real reason I decided to snark on this article? (In truth, I have nothing against Branson.) It's that the article ends with a promotion for one of its publisher's offerings, and the ad begins with the bolded phrase: Want to make extra money outside of your day job?

Still not sure if that constitutes irony or not, but I got a good laugh out of it.

Regardless, sure, success can only be defined by the individual. But having lots of money, no matter what problems it might bring with it, is always better than wondering how you're going to make rent next month.

7 Like • Comment • View 2 comments

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