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Thursday, Apr. 25, 2024

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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 17 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 17 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 17 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

a day 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

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

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
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?

September 12, 2020 at 12:13am

#993134

Drinking about Thinking

Today's prompt is kinda what journaling is supposed to be all about, right?

PROMPT September 12th

Write about something you need to get off your chest. What’s pressing on your mind?

Other than the bloody obvious, stare-in-your-mask-wearing-face bullshit that's consumed us all since somewhere around the beginning of the year, I'm drawing blanks.

I guess that's a good thing. Life, for me, could be -- and inevitably, at some point, will be -- so much worse.

Don't you just love realism? Oh, sure, some may call it pessimism, but I know better.

Yes, I miss being able to travel, but I'm pretty sure that's going to happen at some point (provided, of course, the aforementioned turn for the worse delays itself for just another year or two).

What I miss even more is being able to sit at a bar.

I don't mean just being able to go to a place that sells drinks, sit at a socially-distanced table, and have a few. I've had opportunity to do that. I mean sitting on one of a row of barstools, contemplating the neat lines of fine beverages behind the bartender, and slowly consuming one of them.

Fun fact: Virginia doesn't have bars.

I mean, sure, there are places like what I've just described, but thanks to arcane Prohibition-era laws that have not changed, we have no establishments whose sole purpose is to provide a variety of adult beverages. What we have are:

Restaurants with a bar inside.

Craft breweries / cideries selling their own product exclusively.

Wineries also selling their own product.

State-run liquor stores (fermented beverages can be sold in supermarkets and convenience stores, but not distilled ones).

Of course, this doesn't stop me from going in to a restaurant and pretending it's a bar. They've got the barstools and the liquor lineup, which is more than I can say for Utah. Or... they did before the pandemic; right now, no one's letting anyone sit at a bar. They do try to push food on you, though; the law I mentioned before says something like at least half of an establishment's revenue must come from food service, or they lose their license.

Somehow, though, we get by. Things always change, and even in the past 20 years a lot of the more restrictive rules have been relaxed. Like, I can now order beer for delivery. This was mostly a pandemic-related innovation, and we'll see if it continues. I mean, one of the main purposes of liquor laws is ostensibly to discourage drunk driving, and what better way to do that than by delivering the product to one's own house?

That said, I'm not sure they really want to discourage drunk driving; it's too much of a revenue generator.

So, like I said, I get by. I'm really not looking forward to the colder weather, and not being able to sit outside to order drinks at a restaurant, but I'll muddle through somehow.

Mini-Contest Results!

Surprise! Everyone's a winner today. Because yesterday was my account anniversary, I'm handing out gifts in the form of Merit Badges to everyone who commented yesterday. I won't be making this a regular event, though; this was a special occasion. And it'll probably be at least two weeks before I do another Mini-Contest, to avoid having to deal with CR time restrictions. But I suspect I'll do another "normal" one towards the end of the month.

The following commenters will get their MBs later because I've given them one recently: ⭐Princette♥PengthuluWrites

, Apondia

, and WakeUpAndLive️~🚬🚭2024

. Everyone else who commented yesterday will get theirs soon. Thanks for reading!

7 Like • Comment • View 10 comments

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