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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 13 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 18 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 28, 2020 at 12:21am

#989336

Something is Rotten in Belgium

If anyone's joining us from "July 2020 Blogging Bliss Newsletter - Issue Ninety-One"

: Hi! Everyone else should definitely check out that link, because it features Me. Oh, and some other cool stuff too.

PROMPT July 28th

All month, you’ve been replying to prompts straight from the Challenge War Chest, filled with prompts from previous 30DBC competitors. Today, write three of your own prompts and then reply to one of them in your entry.

I had a disappointing experience yesterday. I've been walking to my local taphouse about once a week since they reopened (patio only) for some food and fine fermented beverage. Someone has to make sure they're still in business for the foreseeable future, and I volunteer as tribute. Anyway, yesterday was Taphouse Day for me. Among other libations, I ordered a Duvel

, because whenever a Belgian beer shows up on draft, I jump on that sucker.

What I got wasn't a Duvel. I know what it's supposed to taste like, and it was just... off. Didn't even taste Belgian. Maybe they got a bad batch, or they mixed up the taps, or something. I also considered the possibility the fault was in my own palate -- sometimes beer just tastes different if you eat certain foods or drink something else first -- but none of the other beers I tried were wrong. Besides, the trademark feature of a Duvel (and a few other Belgians) is a particularly creamy head, and this one was as headless as a horseman.

Only mildly disappointing, to be sure, but I mention it because in all the years I've been a craft beer snob, this is the first time I could tell that something just wasn't right. Well, there was the time a brewer in Colorado had me try what he called an IPA, and I was like, "This isn't bad; it's more like an ESB." "Oh, yeah, it is an ESB but Americans think it'll be bitter, so we call it an IPA." For the record, ESB is "Extra Special Bitter," but the style isn't bitter at all, while IPA (India Pale Ale) does tend to be bitter, so... I mean... what? They're both British styles. Leave it to the Brits to call malty beer "bitter" and label their own invention "India." (There's a story behind that but... later.) And leave it to the Yanks to call a thing something that it's not in an effort to sell more of it.

So, whatever, I had some other good beer and a nice stagger back home, marred only by my neighbor's Rott trying to kill me.

Point of all of this is that yesterday's experiences inform the three prompts I'm supposed to come up with today for the 30DBC.

1) Have you ever been attacked or threatened by someone's pet or a wild animal? If so, what happened? If not, what do you think you'd do?
2) What's the longest distance you've ever walked in one go?
3) Describe a time when you expected one thing and got something else.

I know I only have to talk about one of them, but:

1) The Rott today. I just stood on the sidewalk and stared him down. I was just sober enough to know that dogs take that as a challenge, and just drunk enough not to care. Come at me, mutt. His human corralled him, though.
2) I talked about yesterday. Worked out to something between 6 and 7 miles. The walk to the taphouse is only like a mile and a quarter (seems like more when it's 100F outside, though). If you're a kilometer/Celsius person, do the math; I can't be arsed right now.
And since I've already talked at length about (3), you can read about it above.

6 Like • Comment • View 9 comments

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