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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:

Lazy Writer est 4/24/2008

23 minutes ago
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

about 4 hours ago
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

a day ago
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 Udon Thani

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 Udon Thani

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.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

November 4, 2021 at 9:10am

#1020795

Hide-And-Seek Champions

I vaguely remember when they posted grainy pictures of missing sprogs on milk cartons. I liked to call them the Hide-And-Seek World Champions, because I'm an asshole.

PROMPT November 4^th

We've all heard of people who mysteriously 'go missing'. Tonight, write about a person who 'goes missing'. Someone that you read about in the newspaper or online, but nobody seems to know them, or remember them.

But of course, anyone (not just kids) "going missing" is a serious matter. Sometimes it turns out to be a misunderstanding. Often, especially with older kids or adults, they seem to disappear (I mean, they know where they are) because they want to. Most of the time, with kids, it's another family member; on occasion, it's an actual case of "stranger danger."

And I think most of us have noted a certain bias in local and international reporting when it comes to missing people. Specifically, attractive young white women get all the attention (as with everything else in life), while everyone else is, at best, mentioned somewhere between the obituaries and detergent ads or, at worst, never.

This is not just observation bias on our part, either; someone did an actual study.

I'll call Missing White Woman Syndrome MWWS here. Honestly, the only thing about the study that surprised me was that the disparity they found seemed less than I expected. But that's why we do science - to try to systematically eliminate subjective biases.

The latest example of this was Gabby Petito, who the news just. Would. Not. Stop. Talking. About. And I don't even watch cable news, or have cable; I just caught the edges of the stories here on the internet, and that was enough to make me wonder what real news they were distracting us from. I mean, sure, the case had sensational elements, but I just couldn't help thinking it was an obvious instance of MWWS.

On Maui, a few years ago, this chick

went missing, it made national news, everyone was freaking out about it, and fortunately it ended relatively well. But earlier the same year, these dudes

disappeared. You've never heard of them. Hell, the link I just posted is Maui local news.

Or right here in my town, a hot blonde chick, Morgan Harrington, disappeared from a Metallica concert like 12 years ago now. I don't know; maybe you remember this one, too. Hell, Cosmopolitan magazine did a bit about it, with the headline, and I'm including the link here so you know I'm not joking in any way, A Beautiful Girl Gone Missing

. I mean, you expect "beauty" language from Cosmo, I suppose, but what in the acid fuck does it have to do with anything?

Especially since a couple of years later, Sage Smith disappeared from another part of Charlottesville. Never heard of her? Not surprised. Marginalized trans woman. To their credit, the cops continued to work the case, and from what I can tell it ends just as tragically (though it certainly took a lot longer), but as far as I know, it didn't receive national attention at the time.

Now, I'm not saying that missing human cases must always be treated equally. There are always going to be some more salacious, or mysterious, or disturbing than others -- which was part of the reason for the constant focus on Gabby Petito. Several thousand people "go missing" every year (the exact number depends on definition), and that's a lot to follow. If someone is missing, and there's a chance the public can help, sure - but why make a hiker's disappearance on Maui national news, for instance? It's not like you might accidentally run into her unless you happen to be walking around Hale'akala.

I'm also not saying any missing person case is trivial. All I am saying is that all human life has value; sure, it's worse when kids go missing because they're not as self-sufficient, but everyone who goes missing is going to be missed by someone -- by definition.

5 Like • Comment • View 5 comments

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