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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:

tj-Merry Mischief Maker

about 17 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 22 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 22 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

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

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

July 18, 2024 at 12:31pm

#1074113

All In a Row

Got another "Journalistic Intentions"

[18+] entry today:

Jessica Fox

When it comes time to write on a subject about which I know next to nothing, my obvious first stop is Wikipedia.

Sure, it's not perfect, but is anything? Earning a gold medal in the Olympics is about as close as one can get.

And I do have respect for anyone talented and dedicated enough to do that. I also have respect for the talent and dedication required to be an opera singer, but that doesn't mean I want to subject myself to the experience of sitting through an opera.

As much as I enjoy learning new things, there's just not enough time to be interested in everything. Some things get pushed to the bottom of the queue, like opera or sports.

So while it may shock some people that today is the first time I've ever heard of Jessica Fox, today is the first time I've ever heard of Jessica Fox.

Would I have heard of this medal-collecting canoeist—that is, would some news story about her have impinged itself on my consciousness before now if she were from the US instead of Oz? Maybe. Maybe not. If so, that wouldn't be my fault. A lot of the news I get is from the US, but I also get information from international sources, and it's not like she's from some obscure country with a weird language. Okay, weird language, sure, but Australia is hardly obscure. In any case, I actively avoid sports reporting. It's a practice I inherited from my parents.

I'm sure it's somehow bad that my first thought was "sure, you pretty much have to be an Olympic athlete to outrun/outswim/outrow the local wildlife there." That's gone past the "tired old joke" phase to "always funny." It's especially funny because I'm pretty sure Australians promote the exaggeration in order to keep ugly Americans from wanting to visit.

It's not working on me. I'd love to visit, drop bears and all. The thing that's stopping me is the thought of a 24-hour-plus flight (with connections) cooped up in a flimsy aluminum can with a bunch of American tourists.

For shiggles, though, I just looked up some flights (I had to in order to confirm the duration), and the prices are remarkably reasonable. For riding steerage, anyway. Less than 2000 US dollars for a round trip with one stop. Yes, that's a lot of money, but not bad for flying nearly halfway around the Earth, which, I feel I must reiterate, is round.

But I digress. Remember up there I said I inherited an aversion to sports news from my parents? Apparently, things like that run in the family, because Fox's parents were also world-class paddlers.

I guess you could say they're all in the same boat.

4 Like • Comment • View 3 comments

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