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 13 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 15 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.

May 18, 2020 at 12:07am

#983835

Cleaning Up

So. Many. Possibilities.

PROMPT May 18th

What chore do you most dislike doing? Tell us a creative story about how you might get out of doing it.

I hate having to repeat chores. They me feel like I'm stuck in the Groundhog Day movie.

On a computer, I can usually get around this. I can write, or find, a script or program or Excel spreadsheet to automate most of the tasks. I would rather spend, say, 100 hours automating something than repeating it for 10 hours. That's how much I hate repetitive actions. At least whenever I write the program, I'm always learning something. The task itself? Not so much. I'm not someone who can turn his brain off, or who enjoys mindless activities.

Sure, I can play Skyrim dozens of times, but each time, I approach it in a different way with a different character skillset, and I'm still discovering new things about that game. With chores? All I discover is how much I'd rather be playing video games. Though, true, I have a lousy memory and I do a thorough purge of the house about once a decade, during which time I make all kinds of cool archaeological discoveries.

Naturally, some things just have to be done. Even if I didn't essentially live alone, they have to be done, and I can't expect whoever I'm living with to do all of them. Washing dishes, laundry, cooking, general cleaning, yard work, trash disposal, catbox maintenance, whatever. The worst of these being, I suppose, housecleaning.

I find ways to limit the amount of time I spend on these tasks. I have a dishwasher, washer/dryer, microwave, and so on. I arrange things so I spend the least possible amount of time doing hated chores. I also hire a lawn service and a housecleaning service.

For some reason, it's somewhat socially acceptable to hire a lawn service. They come by, ride around on a mower, and then I pay them. But people freak out about the maid service thing. "You're home all the time. Can't you just clean your own house?"

Can I? Sure. Do I want to? No. Keeping up with stocking all of the cleaning supplies is, by itself, enough to make me meshuggah, let alone having to actually do the work. It's a colossal waste of time and energy for me, and they need the money, so it's a mutually beneficial arrangement.

I'm not a complete pig; I don't leave stuff lying around with food on it, and I absolutely keep up with trash/recycling. But if I could pay someone to do that, too? I'd do it. Sadly, it's unfashionable to keep a full-time servant around like in the old days. That wouldn't stop me, though, if I could afford it.

What I really want is a robot that can take care of all of these things for me. A Roomba just isn't sufficient; I need one with an advanced AI that can, for example, sense when the stove has a spill on it and wipe that shit right up. Like on The Jetsons, only with less attitude. With my luck, though, the robot would end up resenting my lazy ass and go on strike for higher wages and better working conditions, probably right about the same time the sexbot leaves me for a delivery drone.

3 Like • Comment • View 4 comments

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