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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:

GeminiGem of House Lannister

a day ago
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 going to 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 going to 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.

Kåre Enga going to Montana

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

November 10, 2018 at 1:41am

#945262

Essay It Ain't So

https://www.thoughtco.com/write-the-perfect-personal-essay-3858745

The assignment is really quite easy, it's about you after all, so this is your opportunity to shine!

The darkness does not shine. The darkness broods. And maybe smoulders a little bit, but mostly broods.

I always hated writing essays. Probably that's why I went into engineering instead of pursuing a liberal arts degree. No... wait... that was the money.

1. Understand the Composition of an Essay

The five-paragraph essay form was the bane of my high school existence. Well, that and jocks. Well, mostly jocks, but also the five-paragraph essay form. It was especially bad when I had to write one in Latin. Semper ubi sub ubi, et non illegitimati carborundum.

2. Find Inspiration and Ideas

Ever see one of those "how to draw" sketches? Like, "How to draw a puppy."
1. Draw an oval for the body.
2. Draw a smaller oval for the head.
3. Fill in the minor details to make it look like a puppy.

That's what I think of whenever someone urges me to "find inspiration." Like it's that easy. I can't draw worth a damn, so I get stuck on Step 3 and it ends up looking like a Jackson Pollock puppy. I can write well enough, I think, but... "Find inspiration and ideas." Yeah... right. You know what I noticed today? My deck is covered with leaves. I can either let them sit there, or I can rake or blow them off. If I let them sit there, eventually a wind will come by and remove them, or they'll rot away. If I remove them, more will take their place and I'll have to repeat the chore; it's still fall.

That's the extent of my inspiration and ideas for today: justification for being lazy.

(As an aside, it's both heartening and disheartening that this section of the linked article recommends doing something I've been doing for a while, the "core dump" I outlined two entries ago. Heartening because someone else thinks it's a good idea. Disheartening because it was MY IDEA DAMMIT.)

3. Freshen up Your Grammar

My grammars are dead, you MONSTER. Oh, wait, that kind of grammar. Well, that's always been pretty easy for me. That and spelling. This is despite my predilection for incomplete sentences in blog entries, which, in my defense, I know I'm doing; I use them in an attempt to strike a conversational tone.

Several years back, I heard a teacher - an actual, real-life, primary school teacher - say that she doesn't teach spelling or grammar, because "spelling and grammar checkers will take care of any mistakes." No wonder so many people can't tell the difference between "its" and "it's," or "there," "their," and "they're." Fuck off, teacher - spelling and grammar checkers still don't catch those kind of errors, and now they're ubiquitous. The errors, I mean. Not checkers. Damn pronouns and their ambiguous antecedents.

4. Use Your Own Voice and Vocabulary

No, this is a really bad idea. Well, they're right about active vs. passive voice, but to me one of the great things about writing is being able to stretch one's vocabulary, learn new words, and figure out new ways to use old words.

You know what I haven't used for 30 years or more? A thesaurus, that's what. I don't even know any synonyms for thesaurus. Unfortunately, this shows in my writing. My weakness isn't spelling, grammar, or punctuation (though I know those are not perfect), but repeated words in my first drafts. They're hard for me to catch, since I wrote them in the first place. Since I suck at editing, they tend to stay there.

5. Be Specific with Your Descriptions

This... well, this is actually good advice for writing anything.

6. Be Consistent with Your Point of View and Tense

So is this. Goddammit, get back to stupid shit so I can snark on you.

7. Edit, Edit, Edit

Ah, that's better. There is such a thing as overediting, you know. Even if my spell checker doesn't recognize the word "overediting." Anyway, I'm not one to give editing advice. But I know an ad for EssayEdge when I see one, and this is an ad for EssayEdge. Seriously, does everything have to be a freaking commercial?

8. Read

And if you've gotten this far, a) congratulations and b) you already know to do this.

Fortunately, blogging is usually utterly distinct from the personal essay format, at least for me. Here, I'm just trying to make jokes and a point. I'm not trying to sell myself or prove how clever I am (though, to be fair, I am rather clever - at anything except selling myself). If people like it, great; I appreciate that. If not, oh well - I can't please everyone and I quit trying a while back. In any case, I'm fine with improving my skills and learning new ones, but if I'm forced to write in a certain format, it feels like work.

And I'm allergic to work.

Now, to get back to brooding...

7 Like • Comment • View 4 comments

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