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 11 hours ago
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

tj-Merry Mischief Maker

Dec 23, 2024 at 4:55pm
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🎁

Dec 23, 2024 at 12:56pm
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

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

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

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
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?

July 8, 2024 at 9:43am

#1073675

Playing Chicken

I seem to have a fascination with classification questions, especially when it comes to food. I've chimed in on the sandwichness or lack thereof of hot dogs (I say they're tacos); the difference between soup and stew; and how Chicago deep-dish casserole isn't pizza. To name a few.

Now, Cracked raises another classification question:

What About Chicken Salad Actually Qualifies As Salad?
I can’t see through the copious mayonnaise to any solid reasoning

And no, this isn't about how chicken salad is the grown-up version of egg salad.

Summer is upon us, something that happens in about two seconds flat in the Earth’s modern climate. With it comes the barbecue, and with the barbecue comes a culinary curiosity I’ve never understood: chicken salad.

I don't particularly like chicken salad (I like my dead birds warm), but I think I understand it: as the author notes, it's associated with summer, and it's not a hot dish, which makes it a contrast to, say, barbecue ribs or grilled hamburgers. Plus, this is America, and mayonnaise is practically our national food.

I thought at some point after I’d had a taste of the world and started paying my own rent, the idea of calling said chicken mixture a “salad” would come into focus.

Probably also thought you'd have all your shit together and finally understand a New Yorker article. Didn't, did you?

Now, as for why chicken salad is considered a salad, multiple sources chalk it up to the inclusion of “dressing.”

"Dressing" is another point of confusion. In some parts of the US, they call the croutony mixture served with turkey at Thanksgiving "dressing." Most of us call it "stuffing." The practice of actually stuffing turkey with it has fallen out of favor thanks to contamination issues, but calling it "dressing" just won't cut it.

They shut the book there, too, as if they’ve proven something. Excuse my French, but fuck ouef.

That pun would have been way funnier if he'd spelled œuf correctly.

In my world at least, straight-up, jarred mayonnaise holds no claim to the title of dressing.

And yet its inbre(a)d cousin, Miracle Whip, is clearly labeled as "dressing."

A clarification that’s been lost to time would make all this a little clearer, and that’s the idea of a “bonded” or “bound” salad. More traditional salads are known as “composed,” or mixed salads, while bound salads are fashioned into a single substance through a thick agent.

Now, see, I didn't know that, but other sources confirm it, including the link included with the article.

This distinction would be especially useful for salads that live in both worlds, like pasta salad. I, for one, never order pasta salad on a menu because it’s a coin flip between receiving a delightful, refreshing mix of rotini and cherry tomatoes (with perhaps a pesto vinaigrette), and a trowel full of beige, edible mortar.

This is absolute truth. Except, in some cases, for the "edible" part.

The only thing I will say in favor of mayo-based salads is that the rants decrying them as a symptom of American excess are unfair. That’s because such salads have emerged across the world. Russia, in particular, lays a large claim to them, and potato salad is apparently known as ensalata rusa in South America.

I haven't heard such rants. I was always under the impression that it's the polar opposite of "excess." Unless you're using the term in the sense of "I'm using up the excess chicken from last night." No, though I don't care for them much myself, things like potato salad and chicken salad are generally enjoyed by all kinds of people, including the less economically advantaged.

So, I guess, I'll chalk this one up to the inherent ambiguity of the English language, not some culinary conspiracy.

6 Like • Comment • View 3 comments

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