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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10 Most Recent Blog Comments:

Elycia Lee ☮

about 9 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!

2 Like

Wordsmitty ✍️

about 22 hours 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.

1 Like

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.

1 Like

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.

2 Like

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.

2 Like

Annette in France

a day ago
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.

2 Like

Brandiwyn🎶

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

Love it when stars align!

2 Like

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.

1 Like

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.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

January 21, 2020 at 12:03am

#973843

Souvenir

PROMPT January 21st

How much of your own life or the lives of people you know do you put into your writing? Do you mine your past for inspiration, or do you create wholly new places and characters?

I mean, I write science fiction and fantasy.

Still, it's inevitable that some souvenir of my past, some moment of doubt or pain, of joy or satisfaction, whether mine or someone else's, will make its appearance in my fiction. And it should go without saying that blog entries are as honest as I can make them, within the boundaries of an imperfect memory as well as a desire to avoid identifying specific other people in less-than-ideal situations. Well... and also allowing for the occasional hyperbole or other truth-stretching for comedic effect. Never let the facts get in the way of a good joke, I say. Or a bad one. Especially a bad one.

It's inevitable, really, that the past should creep in to any writing, as that is all that is real. The future is unknown outside of a few constraining assumptions, and the present is a geometric point on the timeline, without dimension, an illusion, the limit of the recent past and the immediate future. Yes, only the past is real, but, like the grammatical tense, memory of it is imperfect - I was running somewhere, they were singing some song, she was on her way to the prom when...

The minutiae of the past are sometimes sketchy and unreliable, so I use some memory that seems sturdy as a scaffolding, a framework on which to build the specifics. Like the skeleton of a building, this defines the general shape, and while some details are clear on the blueprints, others I have to make up, or pull from other memories. Some other situations - like someone in free-fall in a spaceship - I obviously have no personal experience with, but even there I rely on memory: memory of scientific descriptions, of books, movies, and TV shows that I thought got it right (most don't).

Or if it's a fantasy world, maybe something from a dream will pop in there: terrifying monsters, shifting landscapes, rivers of metal, forests of feathery hair. Again, all part of my past, even if not a part of consensus reality.

Point is, and this goes back to what I've been saying for some time, there's nothing useless when you're a writer. You never know when something you or someone you know has witnessed, or learned, or dreamed or watched or endured, can be useful in writing, perhaps just as a metaphor or simile, much as sometimes, that spice that's been languishing on the rack might be just the thing to transform a meal from merely good to delicious.

Maybe that's why I tend to keep things around: for spice.

A picture postcard
A folded stub
A program of the play
File away your photographs
Of your holiday

And your mementos
Will turn to dust
But that's the price you pay
For every year's a souvenir
That slowly fades away
Every year's a souvenir
That slowly fades away

8 Like • Comment • View 6 comments

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