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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 30, 2019 at 1:59am

#950746

Challenge Complete

It's the last day of the official competition, and the last War Chest Wednesday, so it's only fitting I repeat this prompt from November. Write a list of at least 5 blogging prompts to add to the Challenge War Chest to be used for future rounds of the 30DBC. Then, use one of your own prompts to write your entry.

This one was inordinately hard for me. I suppose that's only fair, as it is the last prompt of the month, and the others flowed easily. So yeah, I don't think these prompts are all that groundbreaking, but here they are anyway:

1) Write about one thing you want to do before you bite the dust.
2) If you had to go back and change one decision you made, what would it be and why?
3) Which movie and/or TV franchise would you most like to write for?
4) What job do you wish you had?
5) Abraham Lincoln is credited with saying "Better to remain silent and be thought a fool then to speak out and remove all doubt." Prove him right.

So, the prompt I'm going to use is the first one, but I'm pretty sure it's going to address #5 while I'm at it.

I don't know who coined the term "bucket list," and I can't be arsed to find out. I do know that it became the title of a moderately interesting movie with Jack Nicholson and God.

While I've been known to use the phrase from time to time, I usually call it my "fuck-it list." This is because I've already done most of what I set out to do, and have given up on the rest.

It's come to my attention recently that life is much less frustrating if you can separate "things that I cannot control" from "things that I can control," and to focus on the latter while letting go of the former. This is something akin to the infamous Serenity Prayer, which I resent because a) it's a prayer and b) it's associated with AA, and AA is for quitters.

And yet, far be it from me to reject an idea outright, so I started thinking about it.

Let's imagine that I wanted to win a marathon race. That is, to run 42.195km faster than anyone else in the race. This would depend on who else was in the race, and that is something beyond my control; if anyone has two working legs (or prostheses), or is over the age of 18 months or under the age of 105 years, I would not win. By this theory, the only thing I could control would be my own level of fitness.

But the assumption there is that I can control my own level of fitness. I've been walking every day for the past 5 weeks, which is, like, a new record for me for exercise. My walk is about 2.4km and takes approximately 30 minutes, giving me a walking speed of about 5km/hr, maybe a bit less. And when I finish, I'm out of breath, my calves are spasming, and my shins are on fire. Consequently, I cannot imagine walking 42km, let alone running that distance. It's hard to imagine any amount of training that would allow me to even finish a marathon.

Or take another example. Say I want to take a trip to space. How can I make that happen? Well, probably by paying Virgin Galactic a very large sum of money to fire me into a suborbital trajectory that technically takes me 100km up for a fraction of a minute, thus putting me, by definition, in space. Honestly, even if I were a billionaire, this would strike me as a colossal waste of money. There is nothing about this that I can control, except to decide that I don't really want to take a trip to space after all.

So here's the real example: I want to be published. Now, I'm not talking about self-publishing. Anyone can do that. Some can even be successful at it. What I want is for an editor to tell me, "This story is good and it meets our needs so here's some money." (Actually, it's not about the money, but that's part of the package.) And then have at least one person that I don't know purchase the story.

I have no control over publishers' or readers' decisions. The only thing I have control over is my own process: writing, editing, submitting.

But since I'm utter crap at selling myself and lousy at editing, I can't even control that much.

This is why I've given up on a some of my earlier goals.

But hey, at least I'm walking every day.

6 Like • Comment • View 4 comments

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