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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10 Most Recent Blog Comments:

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

JayNaNoOhNo

Nov 5, 2024 at 1:16pm
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

October 7, 2022 at 12:03am

#1038776

Daube Glacé

Every time I think I've heard of everything in some category, like clothing or games or food, something comes along to prove me wrong.

This is a good thing.

Entry #4 for "Journalistic Intentions"

[18+]

Southern Classic: Daube Glacé
Daube glacé is a labor-intensive dish, best reserved for special occasions

Labor-intensive? Well, that leaves me out. I have a simple rule: if it takes longer to prepare than it does to eat, it's not worth it.

While country ham and salami are hardly foreign to New Orleans these days, they were rarities in the along the Gulf Coast two centuries ago. “We can’t hang meats outside here. They rot,” says Isaac Toups, who runs the kitchen at Toups’ Meatery. In the years before the advent of refrigeration, locals had to find other ways to keep the pantry stocked.

My father was born in New Orleans before refrigeration was common. Probably explained why he refused to put air conditioning in the house. Doesn't explain why he didn't know any New Orleans recipes.

This no-refrigeration thing plagued brewers, too. They had to get creative to find ways to cool the wort and keep the final product from getting too warm. But that's for another entry.

As Toups tells it, one of the best-known snacks of old New Orleans owes its existence to just those circumstances. “As any chef knows, when you reduce a stock down to a glace, it lasts longer,” he says.

Oh. Yep. Sure. I knew that.

Okay, no I didn't.

Daube is a nourishing beef and vegetable stew with French roots.

Quelle surprise.

When Creole cooks simmered the leftovers into a sliceable, shelf-stable concentrate, they inadvertently created daube glacé, a meaty aspic most often consumed on crackers and mayonnaise-slicked po’boys.

"Inadvertenty?"

Nowadays, many cooks in New Orleans make daube glacé using reliable store-bought gelatin, rather than the gelatins already present in beef stock and in pigs’ feet—an extra ingredient in some vintage recipes.

As an aside, I always feel an unreasonable sense of amusement whenever some vegetarian who didn't know where gelatin comes from finds out where gelatin comes from.

Daube glacé is a labor-intensive dish, best reserved for special occasions. If you’re in New Orleans, you don’t have to make it yourself: Langenstein’s grocery store offers a fine version.

If there's something that takes a long time to do, someone will find a way to commercialize it. Look up the history of ramen sometime. Or maybe I'll do a thing on that at some point.

The rest of the article is the actual recipe. I don't know what it is about online recipes; they always have to write a PhD dissertation before getting to the how-to part. No. Stop that. Post the recipe first and then do the notes. Or at least keep the intro short and to the point. I hate reading a whole book only to find that, as in this case, the recipe is Way Too Much Work to bother with (in this case, though, they did say so up front).

I just have one more thing to say, though: it's fashionable now to make fun of the gelatin mold creations from the middle of the last century. And, to be fair, some of them were absolutely disgusting. But as is often the case, it comes from a place of privilege. Aspics, like the one in the linked article, preserved food in a time before cheap and easy refrigeration. Hell, even the way we make gelatin now is way, way easier. And that's okay. I like easy. Easy is good; work is bad.

My father would probably smack me for saying that, but whatever. I'm still salty that I didn't get to try any Cajun dishes until I left home.

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