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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 12 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 17 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.

August 7, 2021 at 12:02am

#1015251

In the Past

Sometimes I just gotta go with a Cracked article.

55 Strange Facts About Famous Events From History

Since it's Cracked, I wouldn't put too much stock in the absolute veracity of all of these "facts." I mean, they don't lie on purpose like some websites, but they can't be arsed to do thorough fact-checking any more than I can.

Still, it's worth reading the whole list. I'm only going to comment on some highlights.

1. The French Revolution

Louis XVI and Marie Antoinette fled the palace and tried to go incognito when revolution broke out. But a postman thought he recognized them, and he confirmed his suspicions by comparing the king's face to the one on banknotes.

Nowadays, we have facial recognition software, and you don't have to be a monarch to get recognized by The System. Yet another reason to wear a mask.

7. The Challenger Explosion

Following the explosion, teams spent nine weeks searching a wide area for bits of wreckage. In the process, they stumbled on a duffle bag with 25 kilos of cocaine.

I should point out, because the article doesn't clarify this, that the nose candy probably didn't come from the shuttle, but just happened to be in the wrong place at the wrong time.

15. The Entente Cordiale

In 1904, England and France signed an agreement that ended almost a thousand years of conflict. They did so because King Edward VII wanted to visit French brothels.

I can think of worse reasons to sign a peace treaty.

19. The Hatfields-McCoy Feud

Records are vague about how this famous family feud started, but it now looks like the McCoys suffered from von Hippel-Lindau disease. This genetic condition creates tumors that cause "hair-trigger rage and violent outbursts."

If only they'd had a doctor in the family.

36. North African Campaign

Both sides during World War II left landmines in the African desert -- tens of millions of landmines. The climate preserved them so well that in the 21st century, ISIS dug up minefields as sources for explosives.

I want to know how they decided who was on mine-digging detail.

45. The Age Of The Samurai

High-ranking samurai strapped giant balloons to their backs. They inflated this bag, called a horo, to protect them from arrows.

I have Questions.

54. The Gold Rush

Gold wasn't the only way to make money when settlers headed to California. In 1851 and 1852, the state paid over a million dollars in bounties for killing or maiming Native Americans. One ad offered "$25 for a male body part, whether it was a scalp, a hand, or the whole body; and then $5 for a child or a woman."

I can see how that could easily be abused. I mean, of course it's abuse to start with, but I can see the bounty hunter now: "Here's a scalp, two hands and a body." "But the body is missing both hands and a scalp." "Huh. Go figure. I'll take my $100 in small bills, thanks."

Like I said, just highlights (or as in the case of that last one, lowlights) -- and we could use a little more historical perspective right about now.

5 Like • Comment • View 3 comments

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