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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Write_Mikey_Write!

about 6 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 8 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.

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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').

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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.

July 9, 2021 at 12:02am

#1013323

Heresy

What the hell. Another JAFBG entry. Warning: This entry contains heresy.

Share a controversial opinion...if you dare.

I have loads of controversial opinions. Hell, I've even shared some of them here before. I have noticed, though, that certain controversial opinions are more than just controversial, but will get the holder of the opinion blacklisted (I believe the current term is "cancelled," but as always, I can't remember whether that has one L or two in the US) from social life.

For example, if you say "women shouldn't breast-feed their kids in public," my gods, you will be descended upon in a manner normally reserved for God's judgment upon the Egyptians.

I'm not saying that, by the way, just making a point. I mean, other opinions like "abortion should [not] be legal" might just get you into an argument, but the above will lead to your flesh being ripped from your skeleton and fed to a marauding pack of rabid hyenas.

There are other opinions that'll get you instantly labeled as a racist or *-phobe. Which is stupid, because -phobia implies fear or maybe hatred. Words mean something, you know. You can be against something without fearing (or hating) it. For instance, I have a healthy respect for venomous snakes and don't want one in the house. This doesn't make me ophidiophobic; it just means I don't want a venomous snake in my fucking house. You can also hate something without fearing it, or fear something without hating it. Like, I hate vertical video; I'm not in the least bit frightened of it. I would experience fear if someone pointed a gun at me; I don't hate guns or the person holding one. Excluding situations where the gun-pointer also happens to be someone I happen to hate for other reasons, but right now I can't think of anyone I truly hate. Banks, sure. Cable companies. But not individuals..

But I digress. Here's the actual controversial opinion I'm going to share. Again, heresy warning:

Cats was a good movie.

Look, I'm not saying it was a great movie. But in my opinion (which is, after all, what this is all about), it doesn't deserve nearly the disapprobation that has been heaped upon it.

I went into the movie (late 2019, in the Before Time) as a lark, expecting a giant pile of steaming fresh litter box deposits because that's all anyone was saying about it. Keep in mind I'd seen the stage play it was based on. Twice. Once in DC, once on actual Broadway. But both were long enough ago that I couldn't really give any kind of opinion on how true the movie was to the musical. I guess I recognized the music, and the main catrachers (I don't know if that pun is going to work or not). I thought it was well-acted, with excellent set design, but with hit-or-miss CGI. It doesn't have much of a plot, sure, but neither did the play -- which, I will remind everyone, was an adaptation of a poetry collection by TS Eliot, and the paper-thin plot is the result of ALW going "okay, how can we tie these dispurrate poetic character sketches together?" Weber, like most producers of musicals, was more concerned with spectacle, meowsic, and theatrical trickery than minor details like plot. And that's okay. It's a feature of the genre, not a bug.

My point being that I genuinely enjoyed it, though I wouldn't call it one of my favorite movies. I think it helps that I'm relatively unaffected by the uncanny valley

effect, where things that look almost human freak people out way more than things that look completely human or completely nonhuman. But I'm aware enough of it to know that the movie's characters resided deep in the Uncanny Valley. Not human. Not cat. Not even Khajiit

. Some unholy genetic splice thereof. That, in my estimation, is part of what gave so many viewers a visceral, negative reaction.

A phobia, if you will.

There are also darkly humorous elements in the movie, something that I find pleasing in My sight but a lot of people don't. Dark humor is like food: not everyone gets it.

So there it is: an unpopular, against-the-consensus, controversial opinion, but hopefully not one that will lead to a plague of locusts descending upon me to devour my flesh.

Since I'm home again, I decided to return to my weekly Alamo Drafthouse visits. I could have seen Black Widow, but that will be around for a few weeks, while the movie I chose to see was having its final showing at the Alamo. So I wanted to catch it before I had to stream it, which I probably wouldn't have bothered to do.

One-Sentence Movie Review: In The Heights

Almost as good a musical as Cats.

Rating: 3.5/5

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