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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

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10 Most Recent Blog Comments:

Annette

about 9 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 27, 2019 at 12:25am

#966853

Quote

PROMPT September 27th

Today, the prompt comes from Prosperous Snow celebrating

!

Share a quote from either your favorite author or your favorite book and discuss why you like it.

Anything contemplated for too long, or repeated often enough, loses its impact. So it is with favorite authors, books, and quotes: I've had several over the years, and their meaning has shifted for me.

That's how we get clichés, you know. Every cliché is born as profound poetry. A knife starts life with a gleaming, razor edge; use and familiarity dulls it, inevitably. Knives can be honed, of course; a cliché, once blunted, can never regain their sharpness. But sometimes, if you try, you can remember the feeling it left you with the first time you heard it.

Ask me tomorrow, and I'd probably pick a different quote, a different author. If you'd asked me yesterday, I'd have probably picked a different quote by a different author.

But the night is deep, there's a portentous chill in the air, and October looms, so today's quote comes from Roger Zelazny's A Night in the Lonesome October, a book I mentioned in here some time ago. Days? Weeks? Time morphs.

Such times are rare, such times are fleeting, but always bright when caught, measured, hung, and later regarded in times of adversity, there in the kinder halls of memory, against the flapping of the flames.

Read it slowly. Read it out loud, if you can. Feel the rhythms and the way the words trip over themselves. Contemplate the feelings it evokes.

I'm not even sure I can explain why I like it, which is a shitty position for a writer to be in. But it's not just a struggle to find the right words; it's also something related to what I said about clichés, above: regarding anything too closely, trying to explain it to oneself, well, that turns it into something lesser, and I don't want to do that with this quote.

One of the most absurd plagues ever inflicted upon the literary world is deconstructionism. No, some things should be left as they are, and I think this quote is one of them.

It's even better in the context of the scene it's in, but I don't think the particulars matter. I can apply it to any moment of joy or delight, make it something to help me get through the inevitable darkness.

That's one reason I'm so adamantly opposed to the "live in the moment" philosophy. Sure, sometimes it's nice to forget the bad things that happened in the past, but is that any reason to ignore the good ones? No. No, it is not.

In fact, Zelazny had a quote about that, too: "It is anticipation and recollection that fill the heart—never the sensation of the moment."

And now I've gone way beyond what I intended to say.

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