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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 11 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 11 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 11 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 21 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 10, 2021 at 12:15am

#1009954

Some Mother Time

The prompt is running late again, and I can't stay up this time; I have a dentist appointment at some ungodly cow-milking hour tomorrow morning. I'll edit this at some point later today when the 30DBC prompt shows up, but I don't know when; the appointment could take all morning. Nothing major, just a time-consuming procedure.

Just to be clear, I'm not upset about this. It's just I've been sticking to this just-after-midnight schedule for so long that I feel like I should explain when things don't go according to schedule.

So instead, can I just say how damn relieved I am that Mother's Day is finally behind us for another year? Well, 11 months. Mother's Day creep is getting almost as bad as Christmas creep, starting as it does around late March, these days. Not to mention the crass consumerism the days share.

Look, I get it; everyone has a mother, and most of us want to do something to show our appreciation for her labor (of both kinds). Mine died 22 years ago, though, and I really don't appreciate the reminders every goddamn year. No, I'm not trying to make the observance go away for everyone; I'm just trying to minimize my own exposure to it. I keep thinking I should make a filter on my offsite email to send any email containing any variation of "mom" or "mother" straight to the trash, but I can't even be arsed to put that much effort into it. Besides, chances are, I'd end up trashing something relevant among all the pleas to buy this or that product.

Anyway, it's over, and that's probably the last I have to say about it until next year, absent its inclusion in some prompt or other. No promises about not bitching about Father's Day next month, though.

Edit:

PROMPT May 10th

Think back to a time when you felt completely calm. What made you feel that way?

Beer.

No, really. And I don't even have to think back very far. Just about two hours or so.

As I said above, I had dental work done this morning. It took three hours, after which I went home and slept until the local wore off, at which point I felt just fine. So I did my regular weekly pilgrimage to the local taphouse, a bit later than normal so there weren't a lot of other people around.

I sat on the patio, as has been my tradition since this whole bullshit started. The accursed daystar burned in the sky, but it warmed the air enough so the covered patio felt perfectly comfortable. I ordered a beer and a steak salad.

Now, I know that I've described before that feeling that I get when the weather is perfect, I'm drinking beer, and there's good music playing. I call it beerenity. It is, quite simply, the only time when I can pretend that there is nothing wrong in the world, that everything is okay, things are exactly as they should be.

It's a fragile state, so I nurture it while it lasts. There on the patio - I was the only one at the tables - I felt no pain, had no worries, made no plans. It's the closest I ever come to accepting the idea of "living in the present," because everything in that particular moment conspires to make me feel... good.

Calm.

And there's always one moment that triggers it. At some point, some song will play on the sound system and I'll remember, at least in part, all the other moments of beerenity that I've experienced, as if time has no meaning and it all blends together.

In this case, it was this song.

I've been crazy, couldn't you tell?
I threw stones at the stars, but the whole sky fell
Now I'm covered up in straw, belly up on the table
And I drank and sang and passed in the stable on, on

6 Like • Comment • View 7 comments

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