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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:

🌕 HuntersMoon

about 12 hours ago
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

a day ago
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

🌕 HuntersMoon

May 2, 2024 at 11:37am
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

April 23, 2021 at 12:01am

#1008989

As If It Happened Only Yesterday

Not doing my usual random article thing today. I found out after I posted yesterday that one of my favorite songwriters died on the 19th, so this one's about Jim Steinman.

Jim Steinman obituary
Composer and songwriter who masterminded Meat Loaf’s Bat Out of Hell, one of the biggest-selling albums of all time

I'll let the obituary do most of the work, here. I'll be getting together with a friend of mine on Tuesday, someone who's also a fan, and pour one out for the Master of Melodrama.

Jim Steinman, who has died of kidney failure aged 73, made a spectacular career of being bigger and more bombastic than the rest, and his achievement in masterminding Meat Loaf’s album Bat Out of Hell will guarantee his immortality.

Meat Loaf is, of course, a great singer and performer, and one of those whose career survived having been in Rocky Horror. But he wouldn't have enjoyed nearly the success that he did without Steinman's songwriting.

Bat’s producer, Todd Rundgren, thought the album was supposed to be a parody of Bruce Springsteen – members of Springsteen’s E Street Band played on it – and Steinman did not entirely reject parallels with the Boss. His own songs, Steinman said, “are dream operatic, his are street operatic. He’s more West Side Story and I’m more Clockwork Orange.”

I am, of course, also a fan of Springsteen, and I noticed long ago that they shared a lot of backup musicians. Roy Bittan's piano in particular lent itself just as well to Steinman's operatic compositions as it did to Springsteen's more mainstream rock and roll.

Steinman’s career as a solo artist only managed to encompass the album Bad for Good (1981), which reached the UK Top 10 and spun off the modest hit single Rock and Roll Dreams Come Through, but he was in demand from many directions.

I had that album. Still do, actually. Most of its songs have been redone by Meat Loaf and other artists, because Steinman's voice just wasn't up to signing the checks that his fingers wrote. Still, I have a fondness for the album.

In the 1990s Steinman ventured into musical theatre by collaborating with Andrew Lloyd Webber on Whistle Down the Wind (based on the 1961 film).

Because really, there was only one composer who could out-angst Steinman, and that's Webber.

He reunited with Meat Loaf for the last time for the singer’s album Braver Than We Are (2016).

I hope they finally got over their turbulent past for that. Never got that album, though; it was after albums stopped being a thing, really. But now I'm going to have to track it down. (That's a pun, yes. "Track?" No? No? Damn. Just not in the groove today.)

The obit I linked includes a video of I Would Do Anything for Love (concerning which comments about what "that" is will be received with great disdain), but I thought I'd include a video of the song I rule at, when I have a suitable partner, on the karaoke stage.

It never felt so good, it never felt so right
And we're glowing like the metal on the edge of a knife...

3 Like • Comment

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