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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 28, 2019 at 12:54am

#950612

Schadenfreude

Write about something happy in your life! What’s happened recently that made you smile? What’s the last thing you laughed at?

Life is darkness bleak, a swirling void of colorless numbness spiraling into the eternal event horizon of...

Okay, okay, enough with the angsta rap.

Still, you may have noticed that I'm not one to focus on happiness.

It seems important to many people, though. I don't know if it's just an American thing, since it's right there in our Declaration of Independence along with a lot of rants about King George III. That line - the "pursuit of happiness" - makes it seem like happiness is something to work toward, instead of what it is, which is a state of mind that emerges from other things.

What other things? Well, it depends on the individual, I suppose; that's the whole point. I'm anticipating a lot of "my kids of course!" answers, and if that works for you, great. For me, every time I see some whiny brat in public - provided that I have the option of walking away - I grin like a little bitch because I don't have to deal with that crap.

So, there's something that makes me happy.

Other peoples' misfortune makes me euphoric, as well. Not if it's undeserved, though. I'm never happy to hear that someone's been dealt a crappy hand through no fault of their own. But when I see some skaterat rack himself on a metal handrail, well, endorphins course right through my body and my sense of righteous retribution is satisfied.

There was a story a few days ago about some so-called "Instagram Influencer" (I looked it up and was grumpy for several hours straight because something like that exists) who was trying to take a selfie at the rim of the Grand Canyon and... well, you can guess what happened.

As one wag noted in a comment about that selfie that had me laughing for about a week, "Started out in portrait, ended up in landscape."

Lots of things make me laugh, but that one stands out in recent memory.

Yeah, I realize this makes me a terrible person, but I figured out a long time ago that I'm less angry when I embrace that than when I try to gin up sympathy in myself where none actually exists. But like I said, it has to be an example of karmic justice; someone falling off a cliff when they were just trying to enjoy a nice hike in the outdoors - even though that's something I wouldn't do, myself - is sad. Someone falling off a cliff while being a thrill-seeking attention whore? You're damn right I'm going to laugh.

In the immortal words of Mel Brooks, "Tragedy is when I cut my finger. Comedy is when you fall into an open sewer and die."

I had a job interview with a civil engineering firm many years ago when asking off-the-wall questions was just starting to come into vogue. So, in addition to the standard "What are your salary requirements?" and "What makes this company a good fit for you?" questions, one of the interviewers smiled and asked, "What brings you joy?"

Well, I couldn't exactly answer "schadenfreude" there, so I made up some half-true crap about the satisfaction of seeing my designs come to life and be taken for granted by the general public.

I didn't get the job. I guess I should have answered, "Sewers."

5 Like • Comment • View 4 comments

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