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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 12 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 17 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 17, 2020 at 12:01am

#988362

Driver's Seat

It shouldn't surprise anyone to know that music is, indeed, very important to me.

PROMPT July 17th

How important is the role of music in your life and in your creative process? Do you write to music? If so, what kind and why do you think it helps?

There was a prompt here a while back that asked the age-old question: if you had to choose between losing sight or hearing, which would you choose? And it was a difficult choice because, while I dislike about 75% of all sounds, the other 25% is music and I'd hate to live without that. On the other hand, I couldn't play video games if I were blind.

Anyway, this prompt isn't that one, but I mention that to illustrate my mindset when it comes to sounds. I've known people who insist on having the TV on all the time for "background noise." This is anathema to me. If I want sound in the background, it's going to be music, not some jibber-jabber on the boob tube.

Another thing that surprised me when I found out about it is the number of people who don't listen to lyrics. I seriously can't wrap my head around that. While all aspects of music work together, I need to know what the lyrics are, and they'd better have some meaning or I won't like the song. This doesn't apply to instrumentals, obviously.

I've tried writing with music playing and without, and I can't say that it's made much of a difference. These days, mostly I just listen to music when I feel like it, which is not all the time. I'm perfectly content with silence, and I can usually tune out ambient noise except when the fucking neighbor mows their goddamn lawn three times a week.

There is one situation, though, when music is absolutely essential to me, and that is when I'm driving.

10 years ago this month, when I bought my current car, lots of things sold me on it, but the most important feature to me was its face-melting sound system. For the first time in my life, I wouldn't have to mortgage my house to pay someone to install an aftermarket stereo. One time, I bought a car at auction for $340, an old Toyota that was only firing on three cylinders and had exposed springs in the driver's seat, but it ran, and the very first thing I did was drive across the street to Crutchfield to buy a $900 stereo system with surround-sound speakers and a subwoofer that didn't really fit in the trunk but I made it work anyway.

Priorities, you know.

I know a lot of people prefer to listen to talk radio or audiobooks while driving, but to me those require too much concentration. Music fills the idle hole in my brain that's left over when driving only takes up a portion of my attention (albeit the main portion), while still letting my mind wander sometimes and get ideas.

Trying to imagine doing my cross-country road trips without music is like trying to imagine a movie without actors.

A long time ago, I had the idea to include a different song with every blog entry, but by the time I got back to blogging, other people had already run with the idea, so I only pursue it sometimes. But because it's appropriate, today I'll leave you with this, one of my all-time favorite songs:

So pick up your feet
got to move to the trick of the beat
there is no elite
just take your place in the driver's seat.

5 Like • Comment • View 8 comments

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