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.

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.

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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.

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

November 1, 2019 at 12:08am

#968734

Samhain Night

PROMPT November 1st

I’m sending this prompt in between princesses and spidermen begging at my door for free candy.

If you celebrate Halloween in your part of the world, what are your family’s traditions? What were the popular Halloween costumes in your childhood? Which candy was the most coveted?

Of course, when I was a kid, it was called Samhain and we'd load our pack asses with sacrificial chickens and make the week-long trek over muddy roads to the nearest henge.

Okay, fine, I'm exaggerating. The roads had some rocks on them.

I've lived in the same house for over 23 years now, which is longer than I lived in the house where I grew upspent my childhood. In that quarter of a century, we've had years where greedy, grubbing spooks have shown up for socialist handouts, and years where I got to eat all the candy myself.

This year I'm losing weight, so I didn't buy any candy. If I have to diet, so do the zombies, goddammit. Hey, at least I didn't print up a bunch of "The True Meaning Of Halloween" pamphlets to hand out to convert the little bastards to Paganism.

I'm absolutely boring when it comes to seasonal decorations. Other people on my street put up halfhearted carved gourds for Halloween or a few desultory lights for Yule, and maybe a limp flag for the Fourth of July. But that all seems like w*rk to me, and w*rk is something I go to a lot of trouble to avoid. Especially w*rk that has no functional purpose. Engineer, remember? If it doesn't hold something up or tie something down, it's not worth doing.

My ex liked to decorate, and sometimes I'd even help her in the interest of marital harmony. That worked out so well that she's my ex. So, my family's traditions (hey, my cats count) are to turn off the lights on Halloween evening, take a nap, and pretend to ignore the knocking and the sounds of splattered eggs and thrown toilet paper. This Halloween, though, I didn't have to bother: they issued a tornado watch, it rained, and the winds got up to 50 miles an hour, enough to blow trick-or-treaters right into the next county. So no beggars. Peace. Well, peace except for expecting a gust-blown tree limb to come crashing through my roof (spoiler: it didn't).

As for my childhood? I don't remember. I suppose the usual standbys: ghosts, vampires, cartoon witches. I can't say I remember any particular costume that I or my friends ever wore. Maybe my mom cut holes in a white sheet once in an attempt at a ghost but then thought better of the optics.

And then we come to the biggest advantage of having been an only child: I got to eat ALL the candy. Well, all except for the candy corn. I may not remember a single costume, but I distinctly remember the first time I stuck one of those disgusting lumps of earwax into my unsuspecting gobhole. I think I was four or five. "What the shitting fuck is this piss?" I believe were my exact words after I spit the abomination onto the good carpet. Even my dog wouldn't touch it. So, "which candy was the most coveted?" Anything that wasn't candy corn.

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