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Tuesday, May. 7, 2024

8:17am 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:

🌕 HuntersMoon

a day 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

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?

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

November 23, 2022 at 12:02am

#1040944

To Die Laughing

This one's been hanging out in my queue since October, but whatever. Poe is timeless.

The Edgar Allan Poe Murder Conspiracy

Article is from Cracked, so take it with a grain of gothic black salt.

As the original goth boi, it’s only fitting that Edgar Allan Poe’s death was as mysterious and haunting as one of his stories. Just before he died at age 40, he seemed to drop off the face of the Earth for a week, and his death has been attributed to everything from low blood sugar to murder.

There was a movie called The Raven about 10 years ago, starring John Cusack as Poe. Critically panned and engendering lukewarm audience response at best, I felt like it was severely underrated. Not that it was a great movie, but it didn't suck, either. I think most people missed the point. The movie makes the most sense, I think, if you remember the Poe quote, "All that we see or seem is but a dream within a dream." Or maybe I'm enough of a fan of both Poe and Cusack to have enjoyed it anyway.

15. Missing Poe-son

Oh, how clever. A Poe pun. Well, I shouldn't complain too much; I have every intention of adopting a tomcat just so I can name him Edgar Allan Purr. Bonus points if I can find a black one.

On September 27, 1849, Poe left Richmond, Virginia, where he’d been busy talking his childhood sweetheart into marrying him, for Philadelphia for a job editing a poetry collection (it needed more symbolism or something), after which he intended to head back to New York, where he lived.

Lots of places claim Poe, and for good reason. He belongs to everywhere, but really, he was a Virginian.

14. October 3, 1849

Four days before his death, Poe resurfaced in Baltimore, if you can call the gutter a surface.

Isn't that just basically Baltimore?

13. Poe’s Death

According to the most likely account, he never got it together long enough to explain how a business trip turned into a disoriented game of dress-up before he died on October 7.

Of course it was October.

For we knew not the month was October,
And we marked not the night of the year

12. Poe’s Cause of Death

Cracked's attempts to fit this story into its usual bite-sized countdown chunks seems forced here, so I'm skipping a few; basically, the next several points involve the various ideas about what might have led to his death. There are a lot of them, and as far as I can tell, none of them really fit.

My personal theory? He fell ill from gothic ennui.

The only person who saw Poe alive after he was brought to the hospital was Dr. John Moran, who kept changing his story.

Keep writing unreliable narrators

and you, too, can have your last days confounded by an unreliable narrator.

You know what would be really helpful here? An autopsy. A death certificate. Any records of any kind. None have survived, if they ever existed, and no autopsy was ever performed on a famous writer who died a bizarrely mysterious death. We don’t know, guys. Our money’s on the hospital administration.

Well, this is America we're talking about. Most likely he died of shock after seeing the hospital bill.

To die laughing must be the most glorious of all glorious deaths!
—E. A. Poe

5 Like • Comment • View 1 comment

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