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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

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

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?

March 20, 2024 at 10:30am

#1066614

Not My Baili-Wiki

Well, "Spring is Sprung"

, as they say, so for no reason other than random chance, here's a Wired article in praise of Wikipedia.

Wikipedia Is the Last Best Place on the Internet
People used to think the crowdsourced encyclopedia represented all that was wrong with the web. Now it's a beacon of so much that's right.

Of course, Writing.com is really the Last Best Place on the Internet, but I'll accept Wikipedia as a close second.

Remember when Wikipedia was a joke?

In its first decade of life, the website appeared in as many punch lines as headlines.

I've noted before that WDC came into being prior to Wikipedia. Not by much, mind you. September 2000 and January 2001.

I remember when those years seemed so futuristic. We expected interplanetary travel, jetpacks, flying cars, suborbital transport, and asteroid mining. What we got was the internet.

The article is long, but here's a few select comments.

To confess that you've just repeated a fact you learned on Wikipedia is still to admit something mildly shameful. It's as though all those questions that used to pepper think pieces in the mid-2000s—Will it work? Can it be trusted? Is it better than Encyclopedia Britannica?—are still rhetorical, when they have already been answered, time and again, in the affirmative.

I remember back then, someone took a random sampling of articles from both Wiki and EB and fact-checked the hell out of them. They came in about equal. Of course, that was 20 years ago, and a few things have changed.

It does not plaster itself with advertising, intrude on privacy, or provide a breeding ground for neo-Nazi trolling. Like Instagram, Twitter, and Facebook, it broadcasts user-generated content. Unlike them, it makes its product de-personified, collaborative, and for the general good.

It does do a fundraising event every year, kind of like public radio. I'm not the least bit embarrassed to say that I contribute. Money, that is. I don't have the will to contribute content there.

More than an encyclopedia, Wikipedia has become a community, a library, a constitution, an experiment, a political manifesto—the closest thing there is to an online public square. It is one of the few remaining places that retains the faintly utopian glow of the early World Wide Web. A free encyclopedia encompassing the whole of human knowledge, written almost entirely by unpaid volunteers: Can you believe that was the one that worked?

I have, at times, noted that it's the modern equivalent of the Library of Alexandria. Like that ancient institution, I fully expect it to be overrun and destroyed by the know-nothings, at some point. Until that happens, I continue to use it.

Wikipedia and Britannica do, at least, share a certain lineage. The idea of building a complete compendium of human knowledge has existed for centuries, and there was always talk of finding some better substrate than paper: H. G. Wells thought microfilm might be the key to building what he called the “World Brain”; Thomas Edison bet on wafer-thin slices of nickel.

Wells was a science fiction writer, and Edison was a hack. They were both products of their time and prognosticated the best they could with the technology available to them. Wells couldn't foresee some storage medium denser than microfilm, and there was no way Edison or anyone else (not even Tesla) could have predicted semiconductor technology (or, if they did, it was by mere chance).

There is, as I said, lots more interesting information in the article. One reason I'm sharing this is that I have a tendency to hyperlink Wikipedia entries here, and I wanted to justify that.

Two things can happen with crowdsourcing. Well, more than two, as usual, but at the extremes, you can get the worst of humanity, or the best. As the article notes, Wikipedia isn't perfect. Nothing is. But it represents the best of humanity, while social media usually represents the worst.

6 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
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