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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Wordsmitty ✍️

about 4 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

about 8 hours 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

about 10 hours 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

about 22 hours 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

Lilli Munster 🧿 ☕ 🎃

Sep 24, 2024 at 9:10am
In response to "All Out of Louvre"

Have a wonderful time in France. Have you run into Annette in France yet? She's there too!

2 Like

September 28, 2020 at 12:06am

#994431

Baggage

I'm pretty damn possessive of my possessions.

PROMPT September 28th

If you were forced to eliminate every physical possession from your life with the exception of what could fit into a single backpack, what would you put in it?

1) My laptop, its power cord, mouse, mousepad. Can't live without these things. Why do I have a mouse when I have a laptop? Because I can't stand using the damn trackpad, and besides, how can I game with the trackpad?

2) A metric assload of $100 bills so I can buy more stuff. No, I do not consider this cheating. Money is a possession, and while most of it's just numbers on some bank's balance sheet, I can convert it to a physical possession during business hours.

3) A .45 caliber handgun for when I find the sonofabitch who "forced" me to give up the rest of my possessions, which include somewhat valuable houses that won't fit into any backpack I've ever heard of. I mean, I'm not a violent person, but that could change in the above scenario.

I guess that last one is kind of cheating because I don't currently own a .45, but that's the first thing I'd buy with some of the money.

4) My passport so I can leave the country after retiring the person from (3).

Seriously, though, the only plausible scenario wherein I could see this sort of thing happening would be an imminent natural disaster, like a hurricane or tornado. We don't get many of either in the Virginia Piedmont, but it happens. It's rare enough that I haven't been arsed to put together a dedicated bug-out bag, which is really something I should work on doing, you know, just in case.

Wouldn't really need the cash, because of cards and such, but the laptop is truly essential. And no, there wouldn't actually be a gun involved unless the reason was a zombie invasion, which happens even less often than hurricanes or tornadoes. The passport is for real, though, because it would suck to lose everything and also not have a means to leave the country if I have to. My wallet would go in there, too, except that it's probably in my pocket. Same with my Android.

Unless civilization has completely collapsed, I wouldn't even bother with toiletries or clothing or whatever -- those things are readily available, though I'd miss a few of my T-shirts. If civilization has completely collapsed, though, not much use for the laptop or smartphone, either. And why would anyone assume I'd survive such an event? I'm not the survivalist type. And without a functioning CPAP, I'm not long for the world anyway.

If the point of this exercise is to get us to think about what physical possessions are truly essential in our lives, I guess what that comes down to for me is: money. It's just so damn versatile.

But I do like the laptop.

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