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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

October 14, 2018 at 12:48am

#943386

The Wisdom of the Ages

Time to get into Grumpy Old Man Mode. I'm going to go get my cane so I can shake it at appropriate points.

https://www.becomingminimalist.com/craft/

This article is unmitigated claptrap.

Here are nine ways to begin crafting a life you don’t need to escape:

1. Make Relationships a Priority.

Wrong!

*shakes cane*

Make money a priority.

People will let you down. All of them, eventually. Not all the time, and it's certainly possible to have friends and family, but know that they will let you down. This is like living in Florida - perfectly fine most of the time, if a bit humid and surrounded by crazies, but eventually you'll catch a hurricane. It's perfectly natural, and you'll recover, but it sucks when it happens.

Money, handled properly and intelligently, will never let you down.

2. Remove Unneeded Possessions from Your Home and Life.

Spoken like someone who's never had to worry about replacing shit.

My parents lived through the Great Depression. They never, ever discarded anything that might be useful. My dad's workshop in the basement contained an assortment of screws, nails, springs, hinges, etc. to put hardware stores to shame. When something broke, he'd use the scraps to fix it.

Once you throw away something, and it turns out you need it again, you have to spend money to get it. This is not handling money intelligently. I'm not saying to keep around old pizza boxes or every pasta sauce bottle, but if I had to buy a new tube of superglue every time I needed it because I threw it away after using it once, I'd go broke.

There's also the life cycle thing - I have a working hypothesis that everything goes through three stages: First, it's brand-new and in high demand. Then, for a while (the timing depending on the thing in question), it's commonplace, ordinary, and for most people, disposable. Finally, it's valuable again because it's old and most people have thrown it away. Keep something long enough, and you bridge right over the second stage. It doesn't matter whether it's a home, a car, a soda bottle, a comic book, a stamp, or some random item picked up at a store - at some point, it'll be valuable again.

And finally, I have a crap memory, so "stuff" is the only way I can remember that something happened and how it made me feel at the time.

3. Make Your Work Your Job.

"When your work is also your job, you have achieved a sweet spot in life."

Yeah, and when you're riding a unicorn and smelling its awesome glitter rainbow farts, you've also achieved a sweet spot in life. Utter nonsense. The only purpose of a job is to make money. Save as much as you possibly can, and you'll end up in a place where you no longer need a job. That is the sweet spot in life.

4. Or, See Your Job as Part of Your Work.

Okay, I'll relent a little bit here. A lot of jobs are psychologically damaging. Find one you don't hate, if you can.

5. Guard Your Time.

Yeah, this directly contradicts their point #1. Relationships mean you're running around dealing with other peoples' problems. A little bit of that is okay. Too much, and you have no time to deal with you own crap.

6. Take Care of Yourself.

"What matters at the end of our life is not the house we lived in, the car we drove, or the possessions we purchased. What will matter in the end is how we treated others."

I'll give them this one. Intelligent use of money doesn't mean spending it on things; further, accumulating possessions thinking they'll make you happy never works. And it is important to treat other people well. Still, it doesn't work to deny ourselves the occasional splurge. And I can make the argument that what matters at the end of your life is that you lived it on your terms, not your mother's, and certainly not those of some random new-agey writer on the internet (or some random curmudgeon like me).

7. Appreciate Your Season in Life.

I'll "season" you, you little whippersnapper.

*shakes cane*

8. Understand the Reality of Trials in Life.

Avoid drama at all costs. Remove from your life every possible source of unnecessary drama, even if that source is family. Especially if that source is family. You'll still have "trials," but they'll be a lot easier to deal with if you're not also dealing with your sister's ex-husband's shenanigans or bailing your brother out of jail again.

9. Find Happiness in Your Every Day.

Crap. The best way to be happy is to not think about happiness or try to be happy. Then it comes easily. Forget "mindfulness," forget about trying to "live in the present" (there is no such thing as the present, and the future is unknowable; consequently, only the past is real). Take joy in the simple things, like watching kittens play or seeing other people suffer karmic justice.

Also, I've found that everybody who talks about needing to "escape" has kids. I don't have kids, so I don't feel the need to escape. I like to travel, sure, but I go to places, not escape from the place where I'm living. You can talk about all the joy you get from your kids all you want, but I'm not buying it - I see the problems they cause.

In conclusion, don't be a dick, but also don't be a pushover. Make your own choices. And stay off my lawn.

*shakes cane*

2 Like • Comment • View 3 comments

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