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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Aiva Raine

a day ago
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

April 2, 2023 at 10:25am

#1047344

Revisited: "Judge, Mental"

In the course of picking, at random, an older blog entry to revisit, I ignore anything less than a year old. I figure it needs time to become vintage, and one year is generally enough for that on the internet.

Today, I got my first result from 2022—but it was from early January, so it's more than a year old. As it turns out, I do have something to say about it. The entry was mostly the answer to a former prompt from "JAFBG"

[XGC]; if you're following along, you know I've been working through the current iteration of prompts there.

As for the entry itself, here's the link: "Judge, Mental"

It starts off with a personal update:

Yesterday morning, we got a few inches of ugly, dense, watery sn*w which brought down branches, leaves, trees, and a nearby transformer (the electric kind, not the Michael Bay kind, though I did get to hear it explode). And my home generator picked yesterday to go on strike for higher wages and better working conditions. To be fair, any wage would be higher that what I'm paying it now, but come on, you only have to work like twice a year; get over yourself.

It took me several weeks, as I recall, to find someone to look at the generator. Fortunately, I didn't need it during that time. They did whatever they needed to do, and then, the next time the power went out... the generator failed again. Fortunately, that time wasn't during an intense cold snap.

I think it's finally back in shape, after I called out someone competent. Fortunately, or unfortunately (depending on your perception), it hasn't been fully tested under adverse field conditions, as this winter was mild.

If the power hadn't popped back on in the middle of the night, they'd have had to chip my corpsicle out of the solid block of ice that had once been a house.

I also have a vague recollection that, once I got the central heat working again that early morning, the thermometer on the thermostat said it had gotten all the way down to... 58F. Nowhere near literally freezing; just above, in fact, the ideal temperature for some darker beers and red wines. But enough for me to freeze my nads off.

In my last Comedy newsletter ("The Weather"

), I described with only a little bit of hyperbole how cold my dad kept the house, which you might think prepared me for a life comfortable with persistent hypothermia (my dad certainly thought, mistakenly, that it would toughen me up), but, in fact, the opposite became true.

Look, I live in Virginia. I expect this kind of shit at least once per winter. It doesn't mean I have to like it.

And this year, I found out what I like even less: not having to put up with "this kind of shit" all winter. I mean, sure, it was nice to have only a couple of sub-freezing days, and no sn*w to speak of, but it ain't natural.

Hell, there was an extended period over the winter where it got up to the 70s (F again, of course) during the days. That's warmer than it's expected to be today. Not entirely unusual for that to happen occasionally in a Virginia winter, but the lack of sn*w beyond a few non-sticking flurries was out of the ordinary. It's April, now, obviously, and it's been known to sn*w in April here; we'll see if we get any.

The rest of the entry doesn't really need embellishment; it's all about a thing I'm judgemental about: beer. About the only thing I can say is: I've been working on it, and I think I'm fairly successful in, if not being less judgemental about it, at least being less of a prick.

4 Like • Comment • View 1 comment

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