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Complex Numbers

by Waltz Invictus

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:

Annette

about 10 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

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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