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.

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').

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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 25, 2019 at 12:11am

#963148

Quality

Ask someone you trust the following question and write about their answer: “What are my best qualities and what are my worst qualities?”

There are few people I trust, and one of the downsides of keeping the schedule that I do is that most of them are asleep right now. My housemate is not asleep, but I reasoned that if I didn't like her answer, we'd still have to share a kitchen.

Fortunately, I have a friend two time zones behind me, and we text a lot. So this is her reply (unedited, from phone text):

Okay your best qualities: your geekery, and the fact that you're unashamed to like the things you like, and gain in-depth knowledge of those subjects. From economics, to space, to science fiction, to beer; and finally how your writing is all informed by your interests and the varied knowledge you pick up.

You're one of those people who doesn't stop learning-- you dont make up your mind and snap it shut. I've seen you adjust your opinion on different subjects based on learning new facts, and you always have nuanced opinions. You're always ready to listen to what people have to say.

I should point out that we trust people who tend to see the good in us. Still, what my friend says here pretty much aligns with how I like to think I am, so that felt pretty good.

Then, of course, I had to brace myself. I mean, I know I have flaws - I'm human, or at least pretending to be one - but I can never be sure if what I think are my flaws align with what other people think.

It took her a few minutes, but she finally came up with something.

Oh, I know. You keep saying you'll go back and edit Eidolon and submit it to a publisher and you haven't yet.

Eidolon is a novel I wrote some years ago, a contemporary fantasy story which I think has potential but desperately needs editing. She's read its first draft, as well as the first drafts of much of my meager output.

I told her I was going to go ahead and generalize that to "lousy at follow-through." Again, not something I didn't know. Not proud of it, but it's good to know one's weaknesses.

But wait, she wasn't done.

Oh one last thing good quality: you're the absolute best kind of male feminist. You don't parrot talking points for the sake of looking good; you genuinely see women as people rather than a different species. You have many female friends that you treat with the same dignity and respect you give your male friends.

And that was something I never really thought about. I mean, I know I have this idea that "people are people," regardless of gender, race, nationality, religion, whatever. This means that to me, there are good people and assholes in every demographic, as well as the vast majority in the middle. I don't like to call myself a "feminist," not because I think there's anything wrong with the word or with feminism in general, but because so many dudes have said that they were as a way to win a woman's favor. I don't want to be associated with that type.

Which I guess supports her assertion.

Again, though, I should issue the disclaimer that this is coming from a friend, someone I've known half her life. A person who doesn't like me would probably find way more negatives, or even find a way to turn the positives into negatives. "Can't make up his mind. Too easily swayed, inconsistent. An unmanly exuberance about things he likes. Has pretensions to feminism, but secretly just wants to get laid. Also sucks at doing what he says he's going to do. On the plus side, possesses self-destructive tendencies, so is probably going to die soon."

But I wouldn't hang out with someone who thought that of me. I'm just saying: I may be biased, but so is everyone else.

Also, I tend to be friends with people who text in good English; I only identified one minor typo in the quotes above. Narrow-minded of me, sure, but I have to have some standards.

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