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Sunday, Aug. 18, 2024

7:16pm 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:

Wordsmitty ✍️

a day ago
In response to "Alt-Tablet"

I thought I'd look online and found that "Travel & Leisure" has a very recent review of best tablets for travel. Of course, the top ones are Apple. Article does mention things to look for for travel. If you haven't seen it: https://www.travelandleisure.com/best-tablets-for-travel-8410003

We usually take a small laptop since it's just a wee bit bigger than a tablet and has a real keyboard instead of an on-screen one of most tablets.

Good luck on who you talk to.

1 Like

WakeUpAndLive️~reshuffle👣

a day ago
In response to "Alt-Tablet"

It looks like you have to go to an actual shop and talk with the staff about your wishes. Don't do this online.

1 Like

🌸 pwheeler - love joy peace

Aug 14, 2024 at 3:40pm
In response to "Cat Astrophe"

Glad the meds were there. Bummer about the no refills and road closures.

I'm glad you thought of the compound dosing change to make your and your cat's lives easier. Your vet might never have.

1 Like

Robert Waltz

Aug 14, 2024 at 12:51pm
In response to "Cat Astrophe"

Update: Everything was fine with the pharmacy (except there are no refills on the prescription, so I get to go through this again in less than a month).

But, since something had to go wrong, when I went to my favorite sub place for lunch, half the roads in town were closed for various emergencies.

That's okay. That just means the universe is back to normal.

4 Like

Kåre Enga in Montana

Aug 14, 2024 at 12:31pm
In response to "Cat Astrophe"

Another case of not considering the consumer? Of course, with cats, it's always questionable who's the consumer.

I suspect cats would prefer home visits.

2 Like

WakeUpAndLive️~reshuffle👣

Aug 14, 2024 at 11:25am
In response to "Cat Astrophe"

Annoying that you and your cats are so dependent on vets. Lucrative business. I have to bring Sprout in the end of the month for his teeth. I know already that that will cost me at least 750 euros. Bad teeth! Hopefully, you got your prescription today!

2 Like

🌕 HuntersMoon

Aug 13, 2024 at 10:16am
In response to "Cracking the Code"

With you, Bob, it always comes full circle. BEER!

1 Like

Elisa: Middle Aged Stik

Aug 12, 2024 at 12:15pm
In response to "Lost Soles"

"That's because the power companies are too cheap to bury the lines."

I feel like expense is the least of their problems. Repairs involve a ton of coordination as well, as discussed on the YouTube Channel Practical Engineering. (Hopefully this link works: https://youtu.be/z-wQnWUhX5Y?si=a3PkEA-x3XPEC3KT)

2 Like

Robert Waltz

Aug 11, 2024 at 10:42am
In response to "Revisited: "It's a Trappist!""

Dave Ryan

- already checked that a while back. The passport is good until mid-2026, which is why I really want to go this year.

1 Like

Dave Ryan

Aug 11, 2024 at 10:30am
In response to "Revisited: "It's a Trappist!""

EU countries require a minimum amount of time remaining on your passport:

...your travel document must have been issued within the previous 10 years the day you enter the EU on condition that it is valid until the end of your stay plus an additional 3 months.

I hope you're not too close to expiry!

1 Like

July 13, 2024 at 10:34am

#1073898

Surprise Me

A brief travel planning update:

I met with the travel agent on Wednesday. As a reminder, I'm using a travel agent this time because a) I'm entirely too lazy to coordinate my own itinerary; b) I don't know exactly what I want; and c) I've never done it before, so it'll be a new experience for me.

I told her basically what I wanted to do (wine and beer tourism in France and Belgium), so she suggested three locations in France: Loire, Burgundy, and Paris.

"So you'll fly into Paris and spend... how long there? Five days?" (I'd told her maybe three weeks for the entire trip.)

I'm like, "I'm not exceptionally interested in Paris. The city is dirty, and the people are rude and will be tired of foreign tourists after the Olympics."

I mean, I get flying into Paris. There's a big international airport there, and the other places I want to visit are generally in the northern part of the country. But thinking I want to spend time there is a big assumption.

Then I remembered that I'd heard the Paris craft beer scene had developed nicely in the past few years. Plus, she dangled "reservations at a Michelin-starred restaurant" in my hungry face. (I think they make most of their money from kickbacks, which is fine.) So okay, sure, Paris. Just not a lot of the touristy places. And maybe three days, not five. I know it's an enormous city and you can spend years there without running out of new things to do, but I'd rather focus on other locations.

The rest of the trip is countryside and small towns. Well, mostly. Nothing's detailed yet, but Belgium might involve staying in Brussels, for which I don't have any objection.

The problem with France, I've found, is that there's pretty much nowhere in the entire country that I don't want to spend time in. Well, maybe some of the freezing cold snow-peaked mountain parts. I wouldn't mind visiting them briefly, or seeing them from a warm, comfortable distance, but, as with every other high mountain range, the combination of colder temperatures and lack of air pressure is anathema to me. Plus, I might be expected to "ski," or "hike," or do any number of disgusting outdoor activities.

Yes, I've done it, like when I spent a week at a science camp in the Colorado Rockies. That's how I know it's not for me.

So, now I'm waiting for them to stitch together a draft of a travel plan. I'll get to look at it and change things if I want. I told her, "Don't worry; I like surprises... but only if they're pleasant ones."

She didn't find that nearly as amusing as I did.

5 Like • Comment • View 3 comments

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