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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 13 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 18 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 18 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

a day ago
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

September 16, 2024 at 9:42am

#1076872

Two Much

We all know I like Cracked. This is partly because, like me, they try to be amusing and informational at the same time.

Sometimes, that doesn't work out on one front or the other.

Companies That Make Only Two Wildly Different Products
It’s usually a bad idea for, say, a coffee shop to start selling auto parts

As a business, diversifying your product line is a surefire way to grow your customer base...

Not always.

Some companies, however, decide that they do two things. Two things only. Two wildly different things only.

5. Guinness

It’s not just a coincidence of nomenclature — the Guinness Book of World Records is the same Guinness that produces the world’s carbiest beer.

No.

I mean, yes, originally. Guinness reportedly started the World Records book as a way for pub-goers to settle bets, as the article notes. Later, the publication (which I'll call GWR) got sold to another company, with rights to the name.

That company then eliminated every world record related to drinking, on safety (read: liability) grounds.

While I understand their reasons, this ripped them from their roots. Would you call a piece of paper and a tree the same thing? No. Then GWR has nothing to do with the Irish manufacturers of dark and delicious malt beverage.

Guinness, the brewer, also sells merchandise, and even has showrooms for it. I've been in one in Las Vegas. Well, at least they did pre-pandemic, and I can't be arsed to see if they're still doing that. Point is, though, not only is GWR no longer affiliated with Guinness, but even if they weren't, Guinness would be selling more than two products.

4 Coors

Yep, the company that makes beer as cold as the Rockies is also involved in the production of high-tech ceramics.

I would argue that they don't make beer, but I'm admittedly a snob on the subject.

Also, it's Molson Coors now, and they suck even harder than AB/InBev, which at least has the decency to (mostly) leave craft brewers to their own devices when they Hoover them up.

3 Yamaha

The customers for Yamaha keyboards and motorcycles couldn’t be more different, and technically, they’re not the same company.

As noted, they're not the same company, so this shouldn't count, either. Also, why can't bikers be keyboardists, or vice-versa?

2 Bridgestone

Bridgestone is another Japanese company that successfully divided itself, not out of prudent business sense but for the love of the game — literally.

Tires and golf balls? Come on, they're both round, dimpled, and made of synthetic rubber.

1 Michelin

Speaking of tires, it’s often said that the Michelin tire company created their restaurant rating system to get people to drive more and wear down their tires faster, but it’s a little more complicated than that.

Okay, I'm going to grant them this one.

In 1900, people had to be convinced to buy and drive cars at all, so Michelin began publishing car-specific travel guides that included where to get gas, what time the sun set at different times of year (because there were no street lights), and yes, the best hotels and restaurants.

In the US, at least, there was another, way worse reason to have to know sunset times.

Now you know, once our car-centric society has destroyed the planet and global warming kills us all, you can blame the French.

Technically, the Industrial Revolution only kicked into high gear after Nicolas Léonard Sadi Carnot figured out the whole "thermodynamics" thing, so we might as well blame the French.

1 Like • Comment

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