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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:

Annette

about 11 hours ago
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

a day ago
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

a day ago
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

September 19, 2019 at 12:23am

#966408

Can't Find a Better Man

PROMPT September 19th

Our very own Kit

is getting married today!

Congratulations Kit!

The prompt today comes straight from me:

Write a detailed description of how your significant other (or another loved one) has made you a better person.

First of all,

RUN, KIT! RUN WHILE YOU STILL CAN!

With that out of the way...

Ever notice that it's always "other people" who claim that being a better person means acting less selfishly? In other words, the very people who stand to gain from convincing you that you're better if you consider other people, stand to benefit from you considering other people.

Bit selfish of them, don't you think?

Seriously, though, apart from that, I don't know what qualifies me to be a "better person." Also, I don't have a significant other, or immediate family. I do have friends, of course, and I think they help keep me from egregious errors. My housemate, for example - good friend, but platonic - I'm pretty sure I'd be less diligent about things around the house if I were living alone.

I think about that whenever I get the idea that I want to live alone. I mean, I do want to - never been able to, for one reason or another - but it's probably a bad idea.

Another friend, much younger, keeps me from descending into the quiet chaos of despair. Sometimes it's good for optimists and pessimists to be friends. The optimist (her) keeps the pessimist from giving up completely, and the pessimist (me) keeps the optimist's rose-colored glasses wiped clean of streaks and smudges.

To be specific about one thing we've discussed: I am of the considered opinion that the time to do anything about climate change was about 30 years ago. We didn't do anything, and now it's too late. We're utterly fucked. And I used to care that we're doomed, but I don't anymore. Let the world burn; I won't be around much longer to see the barbecue. Further, at this point, if we did somehow manage to turn things around, the denier brigade would just point at the world and go, "See? Nothing happened. It was all overblown." So yeah, I just want the world to come to a flaming halt so my last words to the deniers could be "WE TOLD YOU SO." And I get these moods where I just want to consume to excess just to help things along.

But having a younger friend makes me want to care, if only for her sake. Not that I do care, but at least I want to, and that's something, I suppose.

I don't consider myself a good person. I mean, I don't kick puppies or treat waitstaff like shit or shoplift or vomit in my Uber rides or anything like that, but that's basic courtesy, nothing to be proud of. So I'm not sure I'd be a worse person without my friends, but I wouldn't care to find out.

4 Like • Comment • View 3 comments

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