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Friday, May. 17, 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:

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
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 ✍️

May 9, 2024 at 1:15pm
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

May 9, 2024 at 10:11am
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

January 5, 2019 at 12:27am

#948917

Baragouin

Write about a time you learned something new. Use and highlight at least 3 words in your entry that are not part of your normal vocabulary and provide your readers with definitions for those words.

I try to learn something new every day.

Many people do, of course. Others actively resist learning, dismissing any new information as inaccurate or false. To be fair, it's not easy to change one's worldview, and new information tends to do that. New facts become baragouin to them: meaningless, irrelevant.

Not me - I want to delve deeper and learn more. When you're a kid, learning comes naturally, like breathing or running. My running days are far behind me, but I do try to keep that childlike openness to new ideas. I'm not talking about jnana , either; I mean real, objective facts.

As a counterpoint, though, I'm essentially lazy, so it's more of a hobby for me than an obsession.

I've told this story before, I know, but I don't remember where or when: in 7th grade, I had a science teacher who insisted that the Earth's gravity was induced by its rotation; in other words, if the planet were to stop rotating, we'd all float off like balloons. I think she was confused by reading science fiction where a space station rotated to create artificial gravity through centripetal force. (No, I'm not defining "centripetal." I'm an engineer. That's been part of my vocabulary for a very long time.) Nothing I said would change her assertion; after all, what knowledge could a 7th grader possibly have that a seasoned public school science teacher did not? Never mind that I was reading better science fiction.

Point is, I learned something that day, even though it was not what she intended to teach: that teachers can be wrong, not just about their opinions on whether or not I should goof off in class (they've always been wrong about that), but about actual, physical facts.

Ever since then, I try not to trust just one source for anything. That said, Wikipedia is not nearly as untrustworthy as some people make it out to be. Sure, errors creep in, but I remember one study that showed it was about as accurate as a printed encyclopedia. You could say that Wikipedia is a hodiernal encyclopedia, and much grander in scope.

So when you learn something, always keep in the back of your mind that it could be wrong. I don't care if the source is a teacher, the internet, or your parents. Or me, for that matter. We're all unreliable narrators. It's just as important to be willing to change your worldview in the face of new information as it is to want to learn new things.

For example, I used the new-to-me word "hodiernal" up there, but I can't be sure I used it correctly. Does "the present day" mean, specifically, 5 January 2019? Or the more general present-day with its technological and social milieu? This is not clear to me. The adjective seems to mostly be used in connection with tenses in writing, though, so I'll be sure to explore it further. When I'm not feeling quite so lazy.

(Incidentally, for anyone who wants to seek out new words and new vocabularizations, I found this

to be essential for creating this entry.)

3 Like • Comment • View 3 comments

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