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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

A signature for exclusive use of winners at the 2019 Quill Awards

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

Show Recent Comments

10 Most Recent Blog Comments:

Elisa the Bunny Stik

about 17 hours ago
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

November 15, 2021 at 12:04am

#1021645

Dark Side of the Moon

Well, at least I have some experience with this one.

PROMPT November 15^th

You and your two best friends are going on a month-long road trip. Where are you going? What three items must be in your luggage for this trip to be a great experience for you.

While I normally road-trip alone, in August of 2017, two of my closest friends and I traveled halfway across the country to see the solar eclipse. It's something I'd always wanted to see, and Missouri is a bit more accessible than Svalbard, which was where the previous eclipse had been visible from. And we could have gone someplace closer, but I wanted to reduce the risk of cloud cover.

That trip wasn't a month, though; it was more like four days. My limit for being in close quarters with someone, in order for us to remain friends, is something like two weeks. But okay, according to the prompt, I'm going on a month-long road trip. Let's set the trip in 2024, because that's when the next solar eclipse crosses parts of the US. Since an eclipse takes about two minutes, and we need the day before to get there and the day after to get back (solar eclipses tend to not be visible at night), that leaves four weeks to do other stuff.

You know what would be fun? To roughly trace the path of that eclipse as a road trip. Obviously, you wouldn't be able to chase the shadow. Even jets have a hard time chasing the shadow. But just taking the time to do it for the hell of it. Pick the spot where you want to actually see the eclipse, and plan accordingly, but also trace the path as best you can while the sun's actually shining. And visit breweries along the way, of course, because that's what I do.

The path of totality across the US can be seen here.

As you can see, the center of the shadow crosses the border from Mexico just southwest of San Antonio (and no wall is going to keep it out). It kisses Oklahoma (ew), darkens Arkansas, then swings through southeast Misery, Illinois, Indiana, and Ohio, before skipping across the Great Lakes, western New York, a bit of Vermont (saying hi to Canada too) and thence across Maine.

Just for comparison, there's also a map that shows both the 2017 and 2024 eclipses here.

So... "What three items must be in your luggage for this trip to be a great experience for you?"

Well, clearly there will need to be more than three items. Hell, I'll need at least three pairs of underpants alone.

But okay, fine, apart from the obvious.

1. Eclipse Glasses. I still have a crapton of these from the 2017 eclipse. Seriously, folks, don't be an utter idiot and look at the sun before or after an eclipse. Or anytime, really. No, the reason I need eye surgery now isn't because I didn't take that advice.

2. Camera. The last time I saw an eclipse, I wanted to simply experience it, not fuck around with camera settings or have anything between my eyeballs and the conjunction (except for Item #1 above). Next time, I want to try to get pictures. No, the camera on a mobile phone won't cut it.

3. GPS. Unbelievably, there are still people who freak out about GPS. Is it perfect? No. Neither are paper maps. But it's freakin' sorcery, and yes, it will even work during a solar eclipse (if the sun spits out a flare, though, all bets are off, which is why I also always carry a road atlas as backup).

Like I said, though, I'll need way more than just those three things, like earplugs so I don't have to listen to my travel companions snoring (I'll bring spares so they don't have to listen to me snoring). And money. And maybe a change of underwear.

...and everything under the sun is in tune
but the sun is eclipsed by the moon...

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