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.

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.

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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.

1 Like

November 22, 2019 at 12:09am

#970185

Missed Connection

PROMPT November 22nd

Write about a missed connection.

I'm convinced that USB connectors exist in four-dimensional space.

You try to plug one in and it doesn't work, so you give it half a turn and try again. It still doesn't work. So you give it another half a turn - rotating it 360° from its original orientation - et voilà! It slides right in, no problem.

A 360° rotation in our normal, everyday universe is the same as a 0° rotation. But in the subatomic realm, you get weird things like electrons and other particles with "spin ½," which only return to their original orientation after a 2*360=720° rotation. One hypothesis for this weirdness is that it's partially rotating in a fourth (or fifth) dimension, a property limited to fermions - and USB connectors. "But you only rotated the USB connector by one and a half turns." Yes, but the first time it didn't work, remember? Another half-turn and it would go back to not working, which was its original orientation.

I'm going to be traveling next month. It's only for six days, but the complication here is that, usually, when I travel, my housemate is here to take care of my cats - and vice-versa. Well, this time, she's going to be away as well, so we needed to arrange for cat-sitting. All my other friends live too far away now, so I opted (this became my responsibility) to go with a professional pet care service. So I did extensive research (translation: I chose the third result on Google Search, not trusting the first two to be anything other than a Search Engine Optimization scam, which is my advice for the day) and called a local place that does that sort of thing.

I spoke with the nice lady and we arranged for a meeting at chez moi so she could meet the cats. This is harder than it sounds because all the cats tend to be shy around strangers. So on the arranged date, which was Wednesday, I took the time to ensure that all the cats were at least inside where there was some chance she'd be able to get to know them, and that their litter boxes weren't too bad. The time for the meeting came - and went, without a sign of the pet sitter.

I called her and, lo, she had utterly forgotten about the meeting. This does not bode well, of course, because what if she forgets when the cats need their food and water? But it's the accursed holiday season, and at this point it's probably too late to pick someone else, so when we finally did connect, yesterday, I wanted some reassurance that someone would actually show up to feed the cats. She assured me that, yes, it was on the calendar, and she'd contact me every day after the deed was done.

My reasoning for going ahead with this was simple: she messed up once, and when you're running a business and mess up once, you do everything in your power to recover a good impression. I thought about installing a few nanny cams for insurance, but then I remembered that I would also get notifications when someone (dis)arms the security system, so I'd have verification that at least someone showed up.

So yeah, sometimes you have to rotate something by more than 360° to get it to fit, but then it runs as smooth as anything.

5 Like • Comment • View 4 comments

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