Complex Numbers (Book)

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Complex Numbers

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/

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Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 20 hours ago
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

about 24 hours ago
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

a day ago
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

a day ago
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
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

Dec 20, 2024 at 6:06pm
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

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

Dec 20, 2024 at 12:58pm
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

December 16, 2024 at 7:51am

#1081213

Fork You Too

Way the hell back in 2018, Quartz published the article / stealth book ad I'm linking today.

Nearly 400 years later, the fork remains at the center of American dining controversy

Does it? Does it really remain at the center of dining controversy? Because I thought that in 2018, and even now, the "center of dining controversy" is how to handle mobile phones at the table.

On June 25, 1633, when governor John Winthrop, a founding father of the Massachusetts Bay Colony, took out a fork, then known as a “split spoon,” at the dinner table, the utensil was dubbed “evil” by the clergy.

While this article is US-centric, and makes no attempt to be otherwise, other sources

show that the fork has been considered a tool of the devil since it was introduced to Europe. This is, naturally, just another in a long list of humans considering anything new and different to be necessarily evil, because we're kinda stupid like that.

Forks were pretty much unheard of during Winthrop’s era. People would use their hands or wooden spoons to eat. The Museum of Fine Arts (MFA) in Boston says that only “a handful of well-to-do colonists,” adopted the use of the fork.

I mean, technically, you're using your hands either way.

When Americans finally started their love affair with the fork, their dining etiquette compared to their international peers became a source of controversy for centuries, whether it’s the way the fork is held, only eating with the fork, or using the “cut-and-switch.“

Oh, no, different countries do things differently. The horror.

During the time it took for Americans to widely start using the fork, dining cutlery was evolving in England. Knives changed to have rounded blade ends, since forks had “assumed the function of the pointed blade,” says Deetz.

I'm betting there were other reasons for the switch, like, maybe, deweaponization?

So if you've ever wondered why some cultures point fork tines up while others point them down, well, the article explains that. Sort of. Unsatisfactorily. Still not mentioned: why formal place settings are the way they are.

Also not mentioned in the article (perhaps one of the books it promotes says something about it, but it's unlikely I'll ever find out) is the abomination known as the spork.

7 Like • Comment • View 1 comment

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