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Monday, Jul. 1, 2024

4:52pm 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:

tj ~ endeavors to persevere!

about 18 hours ago
In response to "Revisited: "Rock you like a...""

I also purchased a generator because our power would go out anytime the wind blew. It seems to have worked, we seldom have power outages now. Living in Minnesota, all we get when the hurricanes push threw are thunder storms and rain. But, it's Minnesota, so thunder storms and rain are normal. This year does seem to be rainier, however.

I'm thinking, after reading this, that I should invest in a couple of rain barrels and bottle the water up. I could probably sell it online to drought stricken people.

1 Like

Kåre Enga in Montana

Jun 29, 2024 at 2:16pm
In response to "Je Voyagerai"

I once was allergic to going on a cruise. But... I should... just for the experience. I've gotten out of my comfort zone for experience.

With the crush of tourists these days any travel should include how much you want to put up with "other people's vacation" as opposed to your own.

1 Like

Lazy Writer est 4/24/2008

Jun 29, 2024 at 1:38pm
In response to "Je Voyagerai"

Happy traveling..be safe.

Elisa: Middle Aged Stik

Jun 29, 2024 at 11:12am
In response to "It Ain't Wrong"

Ain’t apparently begins as amn’t, a contraction for am not, which you can still hear in Ireland and Scotland today

I mean, an abundant number of Scotch and Irish immigrants ended up in the American South, so this tracks.

While a lot of people consider ain’t improper, it’s a very regular and legitimate part of many forms of English, including in Black English (AAVE). Be mindful that judging someone’s use of ain’t as “wrong” can be a very socially loaded act, to say the least.

For some reason, this reminds of one of the reasons I stopped reading Ask A Manager. A bunch of people were getting real uppity about the use of the phrase "baby daddy". Unsurprisingly, many of these people appeared white. One Black person in the comments finally had enough and threw down with this remark:

"I gotta say, as a black woman it grates to have phrases that come out of AAVE be appropriated, assigned negative connotation (likely because they come from black culture), then discarded with prejudice. If you’re using the phrase to conjure up stereotypical imagery, I can get on board with putting an end to that. But there are plenty of people for whom baby daddy or baby mama are not pejorative at all, just descriptors of the relationship in their dialect, and correcting them to “Father of my child” is just another case of denigrating minority speech patterns and legitimate AAVE grammatical constructions and upholding “white is right” standards."

(For more context, check out this link

1 Like

🌕 HuntersMoon

Jun 28, 2024 at 10:54am
In response to "It Ain't Wrong"

Ain't you on a roll today...

3 Like

Adherennium Dr of Phoolishness

Jun 27, 2024 at 11:53am
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

Jun 26, 2024 at 8:16pm
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

Jun 25, 2024 at 9:30am
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

Annette

Jun 23, 2024 at 1:28pm
In response to "Revisited: "Experience""

This is how I coped:

1 Like

June 29, 2024 at 10:51am

#1073318

Je Voyagerai

I thought I'd provide a travel plan update today, after discussing my general idea here a week ago: "Discomfort Zone"

On Monday, I looked at nearby travel agents. Just their websites and Google reviews.

I'm an avid Google reviewer myself, mostly of breweries (writing ability does have some practical use), so I know to take any review with a grain of salt, much like the item reviews here: each is (usually) just one person's opinion and experience, and everyone, reviewer and reviewee alike, has their good days and bad days. Also, one needs to be aware that some 1- and 2-star reviews are competitors trying to steer people away, while some 4- and 5-star reviews are salted by the company itself.

Still, it can be helpful to take a look at reviews all across the spectrum. If there are enough of them, you can be pretty sure there are some genuine experiences in there.

Anyway, one travel agent specifically bills itself as "luxury travel." I'm not elitist enough for that. Another had mediocre reviews at best. I settled on someone who's been active in town for almost as long as I've been here.

Tuesday, I drifted on over there to try to get a feel for what to expect. Sure, I could have called, but it's not far away.

Now, I know some people scoff at the idea of going with a travel agent. Why not just go and experience stuff? Make your own travel plans, your own schedule? Normally, I'd agree. But then I realized: part of the reason I travel is to experience stuff I haven't experienced before. And I've never used a travel agent, so why not experience that for the first time? Besides, I'm entirely too lazy to work out lodging and transportation details myself for a trip to an unfamiliar place.

They gave me a really good idea as to what to expect in terms of process and fees, and promised to get back to me.

On Wednesday, they sent me a few emails, but I had to visit the dentist to get some drilling and crown work done. That shot my whole afternoon (and most of my medical budget), and also the next day while I dealt with the soreness.

Still, I found the energy on Thursday to take a look at the emails, and immediately questioned my decisions when I saw what-all would be required. Passport stuff. Credit card info. Read these T&Cs. Sign here. Sign there. Initials everywhere. (I'm going on a trip, not buying a fucking house.) What kind of trip? What sort of lodging amenities do you want? What's your budget?

"Your vacation is an investment..."

No. No, it is not. An investment is something that's expected to increase in value over time (whether it actually does or not is another issue). Stocks can be investments. A house can be an investment. A car is not, unless we're talking about the classics. A vacation (or, in my case, a voyage, since retirement means permanent vacation to me) is purely spending; the only returns I expect are experiential and emotional.

Words mean things, you know.

On Friday, I called the contact person I'd spoken to and who'd sent me the emails, and she (her name is, amusingly, Karen, and she's a manager, having become the very thing she swore to destroy) assured me that most of these things can be worked out when I meet with the actual travel agent a week from Wednesday.

However, I have no idea what to expect for "budget."

When road-tripping here in the US, I have a pretty good handle on it: I know, to a fair degree of accuracy, what I can expect to spend on gas, food, and lodging each day, and maybe throw in a little extra to try beers at breweries. I'm also not entirely ignorant of what airfare costs, though that varies wildly depending on season and how much discomfort I'm willing to put up with (not a lot, at my age).

I don't want to cheap out, because contrary to popular belief, money does, in fact, buy happiness. Or, well, at least it buys comfort and booze, which is close enough. I also don't want to spend my life savings; I kind of need that for, well, life. Somewhere in the middle would be nice.

What's important to me is that I get value for my money. Like, not spending $100 (or the equivalent in euros) for something that's worth $50.

I figure maybe I can explain that to the agent when I meet with her, and we can work out the details from there. Budget will, of course, help to determine how long the trip lasts and how many different places I can go to. And right now, I'm flexible on those things, as well as on actual dates of travel (I'm hoping for this fall, because I'm definitely not going in the winter, which means if it's not this fall it'll be next spring, and I just don't want to wait that long).

In conclusion, I'm definitely doing this (barring, of course, emergencies). I just don't know any of the details, yet.

4 Like • Comment • View 2 comments

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