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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Annette in France

about 3 hours ago
In response to "It's Hot in The South, Once Again!"

The quote is too small and low contrast to be read.

Elycia Lee ☮

about 13 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

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Wordsmitty ✍️

a day ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

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Annette in France

a day ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

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Elisa: Middle Aged Stik

a day ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

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Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

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Annette in France

Sep 25, 2024 at 3:20pm
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

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Brandiwyn🎶

Sep 25, 2024 at 2:49pm
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

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Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

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Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

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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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