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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:

Kåre Enga in Udon Thani

about 10 hours ago
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

about 10 hours ago
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

about 10 hours ago
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

about 20 hours ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

Aennaytte: Free & Wild in GoT

a day ago
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

May 16, 2022 at 12:05am

#1032463

A Total Eclipse of the Moon

It is a night of a lunar eclipse. The actual full moonination (I just made that up) occurs at 12:14 am (yes, I keep track of these things), which would be when the lunar orb is fully within the shadow of the Earth. That puts it way high up in the sky, to use a technical phrase from astronomy -- perfect for viewing. Usually, during a lunar eclipse, the moon takes on a deep red glow, the reflected light of every sunset and sunrise on our planet simultaneously. It's all really very cosmic.

It's not all that rare; a lunar eclipse happens every few years. I'd say "once in a blue moon," but that would only make the confusion surrounding the definition of a blue moon that much worse. I've ranted about that before. I'll rant about it again. But not today. Common or not, I like to look at these things, especially now since it's the first one since I got new eyeballs.

Naturally, the sky where I am is completely covered by a thick blanket of clouds.

I should probably be more frustrated by this than I actually am, but -- though I hate it when someone goes "well, it could be worse" -- it could be worse. I got the news yesterday (Sunday) that my last remaining aunt, who had a stroke back in February, died over the weekend. She was in her 90s, so it's not like it was totally unexpected or anything, but still sad.

My cousin told me the funeral would be on Wednesday. I went online and started looking for near-last-minute transportation, because I still don't have a car. "Oh, you have to travel in two days? You must be desperate. Here, let us give you the highest price we possibly can." Usually I take a train to NYC, because it's a lot less stressful even if it takes longer. But the trains were booked solid. Still, one cool thing about our little airport here in Charlottesville is that they have daily nonstop flights to La Guardia. That's flights, plural. No puddle-jumping to IAD and getting drunk in the airport bar while waiting for your connection, and lots of options to choose from -- all remarkably pricey on short notice.

Right after I booked the ticket, he called to inform me that, well, no, the funeral would be held in two weeks instead. On Memorial Day weekend.

To his credit, he offered to reimburse me for canceling my really very goddamned expensive booked flight. I mean, seriously, I've flown to Vegas for less. Shit, I've flown to bloody England for less, but that was over a decade ago so maybe it doesn't count. It's pretty close to what I paid for a trip to goddamned Maui.

Problem is -- setting aside for the moment the absolute joy that traveling on Memorial Day weekend is -- I just can't go that weekend. My housemate has her own family plans, and has had them for some time. We have pets. Finding a holiday weekend cat-sitter on short notice is harder than watching an eclipse through the clouds, and I'm not leaving the cats alone.

So it looks like I'll miss the funeral. Hopefully I can take the trip sometime in June or July, go visit my cousin, see the grave where she'll be buried with my mom, her other sister, her brother, and her parents.

Still mostly cloudy here, though I just looked up and saw a single star. It looks like Mars but it's in the wrong place, almost directly overhead. I don't think it's Antares, either; that should be closer to the moon. I can't really tell what it is, because I don't see any other stars to get my bearings.

The whole neighborhood is dark. I think everyone's trying to look at the sky.

Ah. The clouds parted, briefly, and I got a glimpse of the blood-red moon.

Mission accomplished.

Oh, incidentally, the airline completely refunded my ticket price. If I were a total asshole, I'd tell him it was nonrefundable and collect the money, but I'm only a partial asshole.

I'm not entirely in the shadow, you see. Or, well, technically, right now I am, but at least I'm looking at the stars.

6 Like • Comment • View 2 comments

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