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Wednesday, May. 8, 2024

12:13pm 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:

Annette

about an hour 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.

🌕 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

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?

January 17, 2021 at 12:01am

#1002263

Best To Not Think About It

PROMPT January 17th

What do you do to escape or distract yourself from negative thoughts and emotions? How do you take your mind off something you don’t want to think about?

Come on, now, I think everyone already knows my answer to this one.

But really, I have all kinds of avoidance behaviors, not just drinking myself blind. Usually if I immerse myself in a game (one that's a bit of a challenge, not, like, solitaire or whatever), it gets my mind to think about other stuff. Just going off to do something else sometimes breaks the circle of thought.

Thing is, I know that if something in my mind is nagging at me, I should confront it rather than avoid it.

I just don't wanna.

The best strategy, for me, one that is less directly self-confrontational but probably healthier than all of the above, is to start freewriting. Pretty soon my mind wanders and hey, maybe I even get a story out of the deal.

I haven't done that for a while, though -- so avoidance it is!

Mini-Contest Results!

Yeah, I didn't actually expect a lot of responses; it was a tough one. Sumojo

had the only relevant comment with:

I had been asked to be a bridesmaid for the fourth time in my life. The bride was my cousin and I was sure I was asked just to make up an even number.
We had never really liked each other, even as children but I agreed to participate once again. But what I really didn’t want was yet another horrendous bridesmaid’s dress which I’d never be able to wear again even if I altered it. The colours are always atrocious. Lilac or puce. I’m sure that brides select dresses for their bridesmaids to reflect on themselves. To show how beautiful they are and what plain friends she has.
I was bemoaning this fact to my mother, saying what terrible taste my cousin had and I wondered what her wedding gown would look like. “She’ll look like a meringue, I’ll bet.”
I saw my mother’s face go pale and I turned to see my cousin standing right behind me. Whoops!

And I just gotta say, that's a trope that when I see it in a movie or TV show, it never gets old: Character A is talking shit about Character B in front of people, and you see the people suddenly look uncomfortable and their gaze shifts, and Character A finishes with, "...and she's right behind me, isn't she?"

Way more embarrassing in person, I suspect. But hey, have a Merit Badge to take the edge off the shame, Sumojo.

7 Like • Comment • View 8 comments

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