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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 23 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 24 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 24 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?

March 28, 2021 at 12:03am

#1007169

Facts... Maybe?

When you want to learn reliable facts about stuff, you can always turn to... Cracked?

55 Ways You're Picturing History Wrong

Okay, maybe, maybe not. Some of these track with what I know. And no, I'm not going through all 55; you can read the article for that; they're all short blurbs because after all, it's Cracked, not The New Yorker. Which also means it's actually funny.

Ever since 1978, when it became illegal to teach history in schools, all our knowledge on the subject has come from movies, TV shows, and vague chitchat. As a result, we're all buried under misinformation. For example, someone's been spreading weird rumors about how the education system changed in 1978.

Okay, reliable except when they turn to obvious sarcasm.

The article also provides handy links for fact-checking, but of course to be thorough, one should independently verify each claim. If one can be arsed. I can't.

4. Cowboys Hats

American cowboys wore all kinds of hats. Bowler hats were most common. You'd also see sombreros or top hats.

The one time I was at a dude ranch, the only hat I had available was a Panama Jack. None of the Stetsons they sold us city folks fit my head (all those brains take up so much room, you know), so I probably have the distinction of owning the only Panama Jack with a stampede strap.

10. Cavalry Charges

In a movie, when the backup army arrives on horses, they tear through the men or orcs on foot. But in reality, horses smartly refuse to plow through soldiers bearing pikes, so cavalry divisions would dismount before fighting.

Thus once again making one wonder who the truly smart species is.

15. American Cowboys

Cowboys are a Mexican invention. There were vaqueros in Mexico decades before settlers came even to Plymouth. By the 19th century, a third of cowboys in America were Mexican -- and one quarter were Black.

Speaking of cowboys.

Also, I always wondered about that word. I mean, yeah, I knew just enough Spanish to understand what "vaquero" means (along with hola, gracias, and marijuana), but it's gotta confuse non-English-speakers. They ride horses, not cows (yes, I understand they herd cows) and they're generally too old to be "boys." Besides, "cow" is always female. Also, why is there a collective word for every kind of animal except cattle? Like, you can't point at a single cow, bull, or steer and say, "That's a cattle," because cattle is plural. You have to call it a cow, bull, or steer. You don't have that problem with mares, stallions, and geldings; you can point and go "Horsey!"

English is weird.

36. Ninjas

Ninjas didn't dress in black. They disguised themselves in whatever costumes best blended in. Even skulking at night, they didn't wear black, which would stand out like a silhouette.

Fact: Almost every photograph contains at least one ninja.

39. The Library of Alexandria

The burning of the Library of Alexandria really wasn't much of a tragedy. The library had already fallen into disrepair for centuries -- not due to fire but due to budget cuts.

Gosh, that sounds familiar.

46. Martin Luther

Luther didn't actually nail 95 theses to a church door, as cool as that would have been.

Look, this is one of those cases where it's much more amusing to accept the myth, like with George Washington and the cherry tree.

51. Pocahontas

Pocahontas was at most 12 years old when the Jamestown settlers came by. She was also bald and naked, as was customary for her tribe. Good then that she and John Smith didn't really fall in love.

No one tell Disney.

54. The Alamo

The Alamo wasn't a heroic last stand that saved Texas. The rebels only stuck around there because they ignored smart orders, and defending the place didn't help the war effort at all.

Oh, Cracked wants to get banned in Texas, I see.

Actually, I'm only including this one because my favorite drafthouse theater chain is called Alamo because they started in Texas. As I went there quite a bit before everyone started passing dangerous germs around, I became a member of their frequent-flyer club. I'm still amused at the name of the frequent-flyer club: Alamo Victory.

My local Alamo seems to have survived the pandemic and bankruptcy closings that hit some of that chain. I hope it lasts. Soon as I can, I'm going back.

4 Like • Comment • View 5 comments

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