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Saturday, May. 4, 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:

Kåre Enga in Montana

about 10 hours ago
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

about 15 hours ago
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

a day ago
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

July 1, 2020 at 12:01am

#986895

Prenatal Parental

So it's July.

For those of you who might be joining us for "30-Day Blogging Challenge ON HIATUS"

[13+]: Hi! I'm Waltz, and welcome to my award-winning blog. Don't be too put off by the math in the header; it's actually just a metaphor.

So it's fortunate that our first prompt for the month lets me write something that's part real, part imaginary.

PROMPT July 1st

Write a letter to your parents from before your birth. Give them advice about how to raise you and give them a heads up about anything they might struggle with when you come into their lives.

Dear Mom and Dad,

I really want you to adopt me so I don't have to grow up in Indiana, raised by someone I presume is an undergrad who got knocked up by some professor. If it helps, they're both obviously supergeniuses. Wait... IQ is a hereditary trait, right?

So I'll say that raising me is going to be (to use a metaphor you might appreciate, Dad) smooth sailing all the way. Yep, no problems at all. Model child.

...You're not buying it, are you?

Well, get used to it. I lie all the time. Usually I call it "fiction writing," except when I try to tell you that it's not my fault (it probably is actually my fault).

Still, truth is, I at least won't be too terribly disappointing. No time in juvie, and the worst trouble I'll get in at school is saying the F word where a teacher could hear me. Well. That's the worst they'll know about. Thanks for teaching me chemistry, by the way. On a related note, I won't do drugs (that you know of), drive drunk, or emulate my biological father by getting some chick pregnant.

I will, however, eternally be the Class Clown. Look, at least I won't be a mime, okay?

Sorry in advance for nearly burning the house down.

I know you're going to worry about me growing up as an only child in a rural area with few friends nearby. Don't. That worked out for the best. I see people terrified of being alone, and you'll teach me that sometimes, it's better. What friends I have will be good ones -- even if you don't always approve of them. They'll teach me things that you can't.

Not about sports, though. I will always suck at sports. Except maybe tennis. But that's okay; the aforementioned "growing up alone" thing will prompt me, above all else, to like what I like, everyone else be damned.

Word of warning: I will, as a kid, get salty about the whole adoption thing. Don't take it personally. It won't be until I'm older that I'll realize it meant that my parents (that's you) really wanted a child, which is more than a most people can ever know for sure. And I never will try to track down my biological parents. There's no need. One family will be enough for me.

Mom, thanks in advance for teaching me how to love the arts and humanities. Dad, same for teaching me about science and technology. Both will serve me well, and not just for the incident with the school's ventilation system that officially never happened and if it did, it's not my fault.

Okay, no, I'm not going to be the perfect child and you're not going to be perfect parents, but we'll get through it.

I'm just glad neither of you is going to be around for the utter shitshow that is 2020. Spoiler: still no interstellar travel, and boy, could we use some of that right about now.

Love,
Your son,
Robert

14 Like • Comment • View 17 comments

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