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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 16 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.

July 13, 2020 at 12:01am

#988003

Summer Ale

My favorite summer activity is the same as my favorite fall, winter, and spring activity.

PROMPT July 13th

Write about your favorite summer activity.

The only difference is a) where it happens (indoors or outdoors) and b) what kind of beer.

When I was a kid, in the summers I'd relax after a long mammoth hunt by swimming in the bay behind our house. Okay, no, I'm not really that old, but once I start a running joke, I don't know when to quit.

It gets hot in Virginia in the summer. Hot and humid. My dad didn't believe in air conditioning, so during the hottest parts of the summer, I'd cool off in the calm waters. I'd see weekenders out in their sailboats and cabin cruisers, venturing sometimes to the marina next door. We had a garden, and back then I didn't kill plants just by looking at them like I do now, so I'd work in the garden or the field until I just couldn't deal anymore, and jump in the drink.

My feet got covered in crab pinch welts. Curse those arthropod demons.

I don't swim anymore. I don't live next to the water these days, and boating doesn't appeal to me except as a guest on someone else's craft. Too much work. And there's no way I'm going to deal with all the crowds, kids and germs at a public swimming pool.

When I was married, we'd go to the beach in September, when it's still warm but the place is nearly empty, other peoples' kids at school. Never did see the attraction of sitting on the beach doing nothing. If I'm going to do nothing, I might as well do it in the shade or, better yet, in air conditioning. It doesn't help that my skin is as pale as a white rabbit covered in snow, and I utterly despise putting on sunscreen.

I'm not much for separating beer by season; I'll happily drink a stout in summer and a wit in winter. But the yearly cycle of beer styles does have some effect in that the lighter beers tend to be more available in the summer.

My favorite beer season, if not my favorite weather season, is fall. Then, the Oktoberfest lagers and pumpkin ales come out, and most of them are just not available at other times of year. In the winter you have your stouts and spiced beers, and in the spring... well, there's not much special going on in the beer world in spring, except that it's the time when breweries tend to open their outdoor seating after a long winter, and you can sit there enjoying a wide variety in the open air.

But in the summer, a nice pale brew can be refreshing. While I'm not a big fan of IPAs, there are wheat beers, lagers, whites, and other brews of relatively low ABV that suit the season. But again, if I feel like drinking a heavy, high-octane stout in the 90 degree heat? I'll drink one.

So that's my favorite summer activity: drinking beer. Doesn't matter where I am: beach, mountains, suburbs, home... these days, of course, it's mostly at home.

When I can do it again -- if I can do it again -- I'm going to do a summer road trip, visit breweries in exotic locales like Michigan, Texas, or the West Coast. Maybe even Canada if they ever decide to let us barbarians back in. Most of my road trips have been fall or winter, which always runs the risk of accursed snow.

Just as long as I stay out of the direct rays of the blasted daystar and there's a beer at the end of the day.

9 Like • Comment • View 8 comments

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