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 22, 2020 at 12:03am

#973927

Running On Empty

PROMPT January 22nd

Your bags are packed. You have unlimited funds and resources to travel anywhere you want. Where do you go, who do you bring with you, and why?

Thanks, yeah, remind me about how I'm not going to get to go to Scotland with my friend.

There's a part of me that wants to travel, and keep traveling, and never look back. It urges me to go out there, anywhere, everywhere, see all the sights, do all the things, drink all the booze, while I still can.

For what? Asks the other part of me, the part that wants to stay home and run a routine. What's the point? It's not like you have anywhere to run to, or anything to run from. It's comfortable here. And besides, you have cats counting on you. All those travel experiences, sooner or later, all those moments will be lost in time...

So, as with anything else in life, we compromise. I stay home most of the time, but sometimes I go out there, looking out at the road rushing under my wheels. Other times, I fly, even if, sadly, not under my own power.

A few entries ago, I wrote, "There are few people I can get along with for more than a few hours or days." It occurred to me much later that this could be interpreted in at least two ways. What I meant by it was that I don't like to inflict my presence on other people for very long. So, I generally travel alone. I don't have to, though. I'd bring anyone who can put up with me.

As for where? Well, where not would be a more appropriate question. I'd probably stay out of war zones. And there's no point in going where there's no booze. Plus, my idea of "roughing it" is staying in a two-star hotel; camping in the wilderness is a hard pass. So is trekking across Antarctica. Fuck that noise.

That still leaves a lot of ground to cover. And ocean; cruise ships count as "not roughing it."

Some things on my wish list: Trekking across Canada the way I've done with the US - summer only, thanks. The civilized part of Alaska; also summer. Japan, for many reasons, chief among them a particular brand of Japanese whiskey I just can't get in my country. A river cruise down (or up; I don't care) the Danube. A few weeks in France, sampling as much wine as I can. Belgium, for the beer and the food. Germany. Scotland, as I've noted (technically, I've been there, but didn't get to drink any scotch). The Caribbean. Parts of Central America (see above about staying out of war zones). Parts of South America; that is, the parts that don't involve piranha nibbling on my tenders. Australia, New Zealand, Iceland. There are other places, but that's a start. Hell, I'd even consider Antarctica if I can mostly stay on the cruise ship.

And so we come to "why." I'm trying to resist the temptation to leave it at "why not?" Why does anyone do anything, knowing full well that there's only one certain destination, after which everything else you've done won't matter anymore? Well, if nothing else, it'll give me more stuff to write about.

Isn't that enough?

If it takes all night, that'll be all right
If I can get you to smile before I leave
Looking out at the road rushing under my wheels
I don't know how to tell you all just how crazy this life feels
Look around for the friends that I used to turn to to pull me through
Looking into their eyes, I see them running too

Running on (running on empty)
Running on (running blind)
Running on (running into the sun)
But I'm running behind

Honey, you really tempt me
You know the way you look so kind
I'd love to stick around, but I'm running behind
(Running on) You know I don't even know what I'm hoping to find
(Running blind) Running into the sun, but I'm running behind

7 Like • Comment • View 6 comments

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