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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.

December 20, 2021 at 12:02am

#1023429

Ain't Talkin' 'bout Love

Coincidence that this particular article came up today. You'll see why in a minute.

Eddie Van Halen endured a 'horrifying racist environment' before becoming a rock legend
In an interview with Marc Maron, former bandmate David Lee Roth revealed just how painful the experience was for the late artist, who was of Indonesian and Dutch descent.

It would be very weird if articles appropriate to other topics of the day didn't come up every now and then, but this one's almost eerie -- there are about 40 links in my queue, and this is the only one that I recall with the theme of racism, and it just happens to be right after I saw West Side Story, which also deals with racism and is set in the same general era. You know the story. Movie review at the bottom, as usual.

Anyway, the article.

Music fans around the world are mourning the loss of iconic Van Halen rock star Eddie Van Halen.

Yes, this article is from last year. But considering I'm still mourning Leonard Cohen from 2016, it wouldn't surprise me.

And while many today honor his legacy as one of the all-time greatest guitarists, fans are also highlighting past interviews describing his encounters with painful racism and discrimination because of his mixed race in his early years.

Bit of background for me: I've never particularly liked Van Halen's music. I've never particularly hated it, either. It was just kind of there, on the radio. But I recognize that the band was talented, and that a lot of people were big fans. However, I didn't much care about things like the David Lee Roth / Sammy Hagar spat. I only say this to point out that at no time did Eddie Van Halen's ethnicity matter to me one bit. I mean, from the name, I figured he had some Dutch in there, but my favorite musician also has Dutch ancestry, so I didn't think anything of it one way or another.

And I had absolutely no idea that he was part Indonesian.

Van Halen... was the son of Dutch and Indonesian immigrants and spent his childhood in the Netherlands.

It doesn't take much knowledge of history to figure out how that might have happened.

His former bandmate David Lee Roth, a fellow rock superstar, once revealed on the podcast "WTF with Marc Maron" just how painful the experience was for the young Van Halen and his brother, drummer Alex Van Halen.

I would, however, like to point out that from what little I know about Roth, I'm not sure I'd fully trust anything he said about Van Halen. I suppose they might have reconciled at some point, but again, I have no idea and I can't be arsed to look it up. Still, I don't know why he'd make up something like that, and there seems to be some primary-source confirmation later.

He added that the brothers, who were often referred to as "half-breed" in the Netherlands, still met difficult circumstances after immigrating to the U.S.

I'm not exactly surprised.

"My first friends in America were Black," Eddie told the journalist. "It was actually the white people that were the bullies. They would tear up my homework and papers, make me eat playground sand, all those things, and the Black kids stuck up for me."

I really wonder why he said "actually" there. I mean, that's what I'd expect from racism in the US. Who did he expect to be the bullies? Other marginalized people?

There's not much more to the article, just a few more details which you can see for yourself at the link, but since I didn't know about it I figured other people might not, either. Whether you're a Van Halen fan or not -- and like I said, their music didn't usually do it for me -- you gotta admit that they were talented, and everyone loves a rags-to-riches story.

I just hope that someday, we won't have to hear stories about people being picked on for being different. I doubt it, but I can hope. Even if it did provide the impetus for him to become one of the most famous guitarists in rock.

After all, nothing could have annoyed those bullies more. Living well can be the best revenge, or so they say. I wonder how many of them ended up being fans? "Oh, him, yeah, that's the weirdo we used to shove into a locker at school. Dude can shred!"

One-Sentence Movie Review: West Side Story:

Absolutely gorgeous movie of the Oscar-bait variety (not that the Oscars have been worth a damn for many years), but I'm not sure there's anything new to the story, and the whole "horny teens create unnecessary drama and widespread collateral damage" thing has been played out for at least decades, if not longer.

Rating: 4/5

4 Like • Comment • View 2 comments

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