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:

Write_Mikey_Write!

about 11 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 13 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

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.

May 18, 2022 at 12:02am

#1032550

Little Water

First of all, I want to thank everyone involved in this year's Quill awards: nominators, judges, and espeically JayNaNoOhNo

for selecting this blog once again. Also congrats to all the other Quill nominees and winners. I'm grateful. But I'm also pissed off, because that means I have to keep up the quality and avoid slacking off, which violates my ethical principles.

That said, today's link doesn't require a lot of brainpower. In fact, the less, the better.

Why Is Minneapolis-based Tattersall Distilling making vodka for Arby’s?
The fast food chain is releasing an “extremely limited” line of fry-flavored vodkas, and it tapped two Minneapolis companies to help.

I'm sure you'd expect me, a soi-disant connoisseur (goddammit, French lessons) of quality adult beverage, to have Opinions on this. After all, I've come down strongly against Chicago "pizza," Cincinnatti "chili," and several other abominations of the Midwest. And, well, I do have opinions, but it's more complicated than that.

Arby’s really is releasing two variations of fry-flavored vodka, and two Minneapolis liquor companies are helping with the rollout.

Hurk.

Arby’s picked Minneapolis-based Tattersall Distilling to develop the liquor and Surdyk’s to distribute it.

I've only been to Minneapolis once, and I focused on beer; I'd never heard of Tattersall. Some of their stuff

looks quite good. They even have an Aquavit, which is rare in the US, and is an example of yet another name for a distilled spirit that roughly translates to "water of life." Appropriately.

Slated to be available exclusively online starting Nov. 18, the vodka will come in two flavors: curly fry and crinkle fry. And yes, there’s a difference between the two, said Kreidler. Both are potato vodkas, but the crinkle fries are flavored with Kosher salt and sugar, while the curly fries are flavored with cayenne, paprika, onion, and black pepper, he said.

I have a pepper vodka in my stash. Ghost pepper. I keep meaning to make Bloody Marys with it.

Incidentally, there's a persistent misconception that all vodka (which is not "life water" but just "little water") is potato vodka. It's not. You can make vodka from just about anything you can distill: yeast eats sugar, and it's basic chemistry to convert starches into sugars. The whole point of vodka is to distill it so that the taste of the original grain is barely noticeable, if at all.

But then they keep adding flavors to the stuff, like vanilla or chocolate or, as I noted above, ghost pepper. A lot of people like it, as is evidenced by the fact that they keep selling it. For me, the jury's still out.

And yet potato is really the only choice for something like this.

Since the announcement on Tuesday, the response from consumers has been varied. On Instagram, one user decried the vodkas as “heinous swill.” Others accused Tattersall of being a “sell-out.” But there were plenty of social media users who seemed excited at the prospect of fry-flavored liquor.

Well, they got people talking about it and forming opinions before even trying the vodka. Mission accomplished.

“You really can’t claim to be ‘craft’ and then attach yourself to a massive fast food chain,” Keller says. “That doesn’t exactly present well to an existing audience. … Consumer culture sees right through that stuff.”

Yeah, that's Gatekeeping 101.

Now, this article was from last November. I haven't looked into it since then. As it was intended as a limited release, it's probably a -- pun intended, of course -- flash in the pan.

That's okay; I have no burning desire to sample it. And yeah, I do think it sounds like an abomination, but I don't give a shit about the corporate connection. Also, if it sounds good to you, and you can find some? Try it. If it doesn't? Don't drink it.

Just... if someone tries to make Big Mac flavored vodka, don't tell me; I don't want to know.

4 Like • Comment • View 3 comments

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