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.

November 23, 2019 at 12:22am

#970299

Just Breathe

PROMPT November 23rd

Write about writing. What makes you feel inspired to write? What steps do you take to get your words from your head onto the page? What does your editing and rewriting process look like? What have you learned from fellow writers?

Inspiration is a funny thing. If I always waited for inspiration to write, I wouldn't write much. Certainly not every day. I don't get inspired often, but once I commit to start writing, somehow I almost always come up with something to say. Sometimes even something funny or inspiring, but not always.

The word "inspiration" etymologically has the sense of "spiritual guidance," or "divine guidance." But the Latin root, spirare, was probably far more mundane: it just means "to breathe," and the word inspire can be rendered as "to breathe into." The connection between breath and spirit is an ancient one, and it figures in ancient Hebrew writings as well, most famously the part where God breathed life into clay to create a human. The dividing line between the living and the dead was seen as that the former breathe while the latter do not. Of course it's not really that simple - we can stop breathing for many seconds or even a few minutes and survive, under certain circumstances - but the metaphorical connection remains.

Obviously, I don't accept the notion of divine guidance. It's all in my head, even if triggered by external events. Lots of things can spark the urge to write. Perhaps oddly, one of these things is seeing, reading, or hearing a badly written story. "I could do better than that!" and then I proceed to probably not do better than that, but at least it got me writing.

But like I said, inspiration isn't a requirement for writing. Nor should it be. Like, when I started this blog entry, I didn't know where I would go with it. Nor did I really feel like writing. I still don't, because there are other things begging for my attention (cats, video games, mild hunger, desire for a cigar and a whiskey, the Netflix binge I'm in the middle of, sleep, etc.) but if there's one thing I've learned from other writers - both amateur and professional - it's this: a writer writes. If you don't write, you are, by definition, not a writer. You don't have to be published, you don't have to be good, and you don't even have to have your words seen by others. But if you write, you're a writer. Hooray for tautology!

A writer also edits, but I kind of suck at that with my own writing. I could edit other peoples' writing, but I often suffer from the delusion that I can write something, give it a quick once-over to check for egregious grammar, spelling, punctuation, and style mistakes, and then I'm done. I'm wrong about that, of course, but that doesn't stop me from losing interest. Once it's written, it's written, and that's that. There's always someth- SQUIRREL!

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