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 8 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.

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Adherennium Plotting something

about 10 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.

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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.

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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.

June 5, 2021 at 12:01am

#1011329

Random Access Memory

Entry #2 of 8 for "Journalistic Intentions"

[18+]. Today we're going to talk about... uh... what were we going to talk about? Oh yeah. Memory.

Memory fails us these days

My memory was questionable even in the Before Times. Like, 20 years ago or more, I used to have a mind like a steel safe when it came to jokes. I could hear a joke once and reliably repeat it.

Music was a good one, too. Lyrics, writers, performers, year of production, hell, even producers -- a whole slew of trivial metadata for each of a bunch of different songs.

What changed? Not age. I know I bang on about being old, but I'm not that old, not yet anyway. No, it was the internet. With an entire world's worth of information at my fingertips, I knew I could forget a lot of things and still consult the Great Oracle for anything I'd forgotten, and besides, even Wikipedia is way more accurate than my memory.

But it made me realize that for me at least, the key to remembering things is emotion.

Give me a bunch of dry facts and figures, and I'll forget them almost instantly. Oh, sure, if I drill them enough I can remember them, like even now I can remember the basic strategy for blackjack even though I haven't gone gambling in something like two years. But if something is a joke, it triggers my emotional "humor" response, so I can remember it. With music, well, I long ago offloaded my other emotions onto music anyway, so it makes sense that I'd remember anything associated with that art, humorous or not.

But if I can make a joke out of something that's not inherently funny, well, boom, there it is, stored in my long-term memory. It's how I could remember things like organic chemistry formulae; I'd make puns about it in my head and dredge them up during a test. I've since forgotten most of what I learned, but it worked at the time.

I wonder, now, why I don't use that more often -- turning everything into a joke. Probably because, all my life, people have sneered at me, "Everything's a joke to you, isn't it?" Well, yeah, it is; that's how I remember it. I have long had this image of me going to trial (for, obviously, something I didn't do) and making an offhand joke about it. I imagine the judge going, "What do you think you are, some sort of comedian?"

"Uh... actually, yes?"

It's like when I did my movie review yesterday. Okay, so, when it came out, I saw the first A Quiet Place. Thing is, I don't remember much about it, because while I recall it was a well-shot and beautifully put-together movie, I couldn't recall a detail of it if you'd put a gun to my head. I think it's because I didn't have a real emotional reaction to it. I remember appreciating it at the time, but... something about having to be quiet because the monsters were blind but had excellent hearing? That's about it.

Hence my joke review yesterday. Give it a year, though, and I'll probably have forgotten the whole movie. That's not a commentary on the film; it was pretty good. It's just that the only emotion it induced in me was the occasional shock of a jump scare. But what I will remember (probably) is how clever I thought I was at turning "silence" into the review.

I don't have many actual phobias in life. I mean, the things that most people are afraid of, like snakes or spiders, well, they have the capacity to startle me, but I'm not frightened of them exactly (the venomous kinds get my respect). Heights invigorate me, and while I'm not a big fan of crowds, I can deal with them. Wide-open spaces, tiny closed dark spaces? Meh, whatever. Needles? Big deal. There's a deep-seated fear in me of anything touching my eyeballs, though, and that's probably why the Universe is fucking chortling right now about me probably having to get cataract surgery, but that's about it for phobias... except for losing my memory.

I'm not sure that particular fear is entirely irrational; after all, I spent 20 years dealing with my parents' profound memory loss. Sequentially. As in, right after my mom died with dementia, my dad was diagnosed with Alzheimer's. Now, I'm well aware I don't have their genes, but that doesn't mean I won't lose everything that makes me me.

At least with cataract surgery, I can be pretty sure that if I can face that particular fear, once it's done, it's done, and my vision will be (partially) restored. There's still no treatment for dementia. Honestly, I'd rather die a quick, earlier, painful death by heart attack than waste away for a decade in some hole somewhere, not knowing who or where I am.

All of which is to say that I don't really sweat the small memory glitches. They're annoying, but not worrisome, not yet anyway. As they say, forgetting where you put your keys is normal. Forgetting what keys are is a problem.

Meanwhile, I try to get enough sleep, avoid stress (and drama of all sorts), and mostly I just have to repeat language lessons more than the average person in order to get the material to stick in my gray matter. For everything else, I'll just keep making jokes for as long as I can.

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