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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

December 18, 2019 at 12:02am

#971632

Red Queen's Race

While we're on the subject of weight loss...

https://www.vox.com/2016/4/28/11518804/weight-loss-exercise-myth-burn-calories

Why you shouldn't exercise to lose weight, explained with 60+ studies

Oh look, another "You're Doing It Wrong" article! - or is it?

"I'm going to make you work hard," a blonde and perfectly muscled fitness instructor screamed at me in a recent spinning class, "so you can have that second drink at happy hour!"

Remember yesterday when I said I wouldn't be caught dead in a spin(ning) class? This reinforces that.

Anyway, the article dives into some science, much of which could stand to be replicated or at least extended. When it comes to nutrition (or, in this case, exercise) science, I approach it with a healthy (pun intended, as always) dose of skepticism.

And I'm not going to quote a lot from it. Instead, I'm just going to summarize:

Exercise is good (and necessary), but it probably isn't enough, on its own, for losing weight.

This tracks with my own experience, but of course my own experience is a data point of one and when it comes to fitness, I always find out later I've been lying to myself. So I don't trust my own experience, either.

Still, it was true for me that diet alone, without additional exercise (that is, more than what it takes to walk from the couch to the bathroom and back again a few times a day) doesn't work. It requires both.

So what's the point of exercise? I ask myself that every time I get on the elliptical trainer, and I have to remind myself that it makes me feel less dumb and helps fend off depression. That alone is usually reason enough to keep going; any weight loss benefits are icing on the donut. Mmmmm... donut... *drool*

Ahem. Anyway. That works for me until it doesn't, and then I get back into the funk of "I'm depressed." "I should exercise." "I don't feel like it." "But it'll make you feel better." "I don't want to feel better." "But I hate being like this." "So? Shut up and have another bottle of tequila."

Yes, I talk to myself like that when I'm depressed. Does it help? No.

This article, to get back to the point, still doesn't address the question I had yesterday: So what happens if I reach my goal weight?

I mean, this can't be a fully linear process, can it? Like, say you're losing a pound a week. Just as an example. Somehow, you manage to do this regularly and consistently. But there's got to be a limit, right? Else you waste away to nothing (which, now I think of it, would make an excellent story- shit, Stephen King already did it). You keep eating less and less and exercising more and more, in order to keep that pound-a-week thing going, and at some point, it turns into the Red Queen's Race - it takes all your energy just to stand still.

That's what worries me, if I'm being honest. That there's no end to this self-deprivation; that I'm consigned to a lifetime of gray purgatory. They say success requires a lifestyle change, and while I'm perfectly okay with some lifestyle changes, especially if I know that I can relax at some point... some things just aren't worth the rewards.

It's frustrating, really.

3 Like • Comment

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