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Thursday, May. 9, 2024

11:18am EDT

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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:

Elisa the Bunny Stik

about an hour ago
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

about 20 hours ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

a day ago
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
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

May 4, 2024 at 5:42pm
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

February 25, 2024 at 9:53am

#1064849

Revisited: "Cheese? What Kind of Cheese? I Want Brie"

In September of 2020, WDC celebrated 20 years of online activity, and my account reached its 16th anniversary. Today's throwback reminded me of this, because it was from the beginning of that month: "Cheese? What Kind of Cheese? I Want Brie"

Hm. Another WDC birthday week. That means I'll be 16 soon.

Obviously, that means that, in about six months, I'll be turning 20. Damn, I can't wait until my account can legally drink. No, I mean I literally can't wait; I do it anyway.

The linked entry was a response to a prompt from "30-Day Blogging Challenge ON HIATUS"

[13+], which I miss, but I have some idea of the amount of work involved, which makes me shudder to think about. The prompt was, in part: "I know this is cheesy, but I have to do it... In your entry today, write about what you love about Writing.Com."

Hence the "cheese" reference in the title.

You know, my hesitation on prompts like this is not that it's cheesy. I can do cheesy. It's that I've been here for just short of 16 years, and no matter how much I try, there is no way I wouldn't forget someone significant if I tried to list all of the people who are important to me here.

Obviously, it's 3.5 years later now. But my attitude on that subject hasn't changed: better to snub everyone equally than to risk snubbing one individual when creating a list of usernames.

I've been on the other side of this, of course. Someone I consider a friend will list the people that mean the most to them on WDC, and I'm not on it. Rationally, I know I'm not everyone's favorite (nor do I seek to be). Monkey brain, though, feels slighted at being left out. I don't want anyone else feeling that way, so, like I said back then:

Everyone that I've interacted with over the years -- occasionally unpleasantly, usually quite the opposite -- has helped to make me what I am today. That includes you, since you're reading this.

One of the major reasons I do these Revisited entries is to see what's changed since the original entry. In this case, it's not much.

Just time.

Fortunately, some cheeses age better than others.

2 Like • Comment • View 2 comments

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