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!

a day 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

a day 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 6, 2019 at 12:16am

#958308

Room for Improvement

Regarding your craft of writing, is there something specific you want to improve on or give more attention? What steps will you take to motivate yourself?

The best drummer in the world is commonly accepted to be Neil Peart from Rush. Word is that there was a magazine about drummers that, every year, picked a "Best Drummer" kind of like Time's Person of the Year, and every year for some time, Peart was selected. This got boring, so they changed the award to something like "Best Drummer, Apart From Neil Peart."

I mention this because a few years back, I heard that Neil Peart was taking drumming lessons.

Writing is like that. I don't care if you're JK Rowling, Stephen King, or William fucking Shakespeare, there is always room for improvement, and one should always take that opportunity. But to do that, it helps to know what aspects of writing are your weak points - and there are always weak points. Plotting, characterization, word choice, pacing, whatever.

Most of us, I think, suck at knowing what our actual weak points are - that's where reviewing comes in - but even if you end up working on something you're already good at, you can still become better. The problem with reviews, by the way - or, well, one of the problems - is that we are all subject to the cognitive bias that I forget the name of, the one where criticism or facts can't change your mind about things. So the first thing to do is to work to overcome that particular bias.

For me, one thing I keep seeing in reviews is that I repeat certain words and phrases. It's annoying, because I make a conscious effort not to, but the redundancy creeps in anyway. The worst thing about it is that I don't catch it myself. I can usually - but not always - catch point of view problems, tense issues, spelling and grammar flubs, etc., on a re-reading, but for some reason I have a blind spot when it comes to repetition.

So that's what I want to work on. If anyone reading this ends up reviewing one of my thingies, now you'll be more aware of repetition when you see it.

My other problem, though, goes back to the second question in today's prompt: motivation. I can barely motivate myself to write, most days, and while I have a near-constant desire to improve many things, not just writing, it's harder outside of, say, a video game. There, you know when you level up. In real life, you have to guess at it.

Maybe if I treat it like I do exercise - but even in that activity, I can kind of tell when I've leveled up. My running resistance level becomes too easy, so I kick it up a notch. I do 15 reps at, say, 60 pounds, no problem, so next time I do 10 reps at 65 and work my way back up to 15 at that weight. That sort of thing. With writing, it's not so easy. I feel like I'm decent at it, and yet I still write some things that are obviously just throwaway, phoned-in pieces, amateur-level. And that doesn't even take into account my examples of purposely silly output.

The motivation thing harks back to something I wrote here yesterday, about being complacent. Thing is, I'm not complacent about my writing the way I am about other things in life. I want to get better. I think I know how to get better. The only thing left to do is the practice, and that's where I lack motivation. What to do about that? Well, just write anyway, I think - motivated or not.

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