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Friday, May. 10, 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:

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

May 22, 2021 at 12:02am

#1010546

A Challenge

PROMPT May 22nd

Write about the biggest challenge you have faced and how you overcame it.

Superlatives can be tricky.

Most embarrassing moment? Greatest fear overcome? Worst mistake? Biggest challenge? All of these things depend on elapsed time since the incident, current situation, and a memory that's inherently faulty.

It's entirely possible that my biggest challenge was learning to walk, a thing that almost all of us have accomplished, but I have only the vaguest memories of that period of my life. Or perhaps it was the opposite: my parents, like I suspect most parents, spent the first three years of my life teaching me to walk and talk, and the next 15 telling me to sit down and shut up. Doing so is a challenge for a kid.

Some time after that, though, I went to college. Now, as you know, I'm a supergenius, so you'd think college would have been easy for me. It was not. Intelligence (I might be overstating mine to some degree) isn't correlated with the drive to do the necessary work to develop it. In other words, I was too busy playing video games learning to drink (not simultaneously; I still suck at that combined skill) to concentrate on coursework. I passed. Eventually. Just barely.

But I did learn one important thing, which was how to focus on learning stuff so I could pass exams. One might argue that this is a relatively unnecessary skill after college, but this is not the case for engineers. So several years later, I had to take the professional engineering (PE) exam, which is not an easy test. Well, I suppose it is for some people, but given a choice between anything resembling work, and playing a video game, I'll play a video game because I'm inherently lazy. Okay, I didn't "have to" take the exam, but having that certification meant more money which I could then use to buy video games and booze.

So when it came time to schedule my PE exam, I buckled down and (mostly) resisted the urge to play video games or drink beer when I should be studying. This gave me skills that the social atmosphere of university never did, which was to find ways to enjoy learning, and to focus on a goal, not my immediate satisfaction. And so I did, and I passed the exam on the first try. To this day, I enjoy learning almost as much as I enjoy those other things. Giving up instant gratification for future rewards, well, I'm still not very good at that.

And then, once it was over, but before I found out the results, I spent a week doing nothing but playing video games in my spare time. Not drinking. Like I said, for me the two are mutually exclusive.

Right now, I'd call that my biggest challenge thus far. Ask me tomorrow, though, and I'd probably pick "losing weight" or "putting the video game on pause long enough to do my taxes." I don't know; I'm not big on remembering the challenge, only the results.

It's also entirely possible that, in the right mood, I would admit that my greatest challenges were ones that I did not end up overcoming. But I'm not in that mood right now. Maybe another time.

7 Like • Comment • View 5 comments

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