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Tuesday, Sep. 17, 2024

2:25pm 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:

🌕 HuntersMoon

about 3 hours ago
In response to "Uncovered"

I get it... communal bathing/uncovered.

Oh, wait...

1 Like

Writer_Mike

Sep 14, 2024 at 5:06pm
In response to "One Thing In Common"

I've no doubt you'll be fine with your knowledge of French, however limited you think it may be. After all, you've been working on it since face masks were de rigueur. When I was stationed in Germany, a small group of us ventured across the Rhine into France - Strasbourg, to be exact. One of our number claimed a working knowledge of the local lingo, so we wandered into a small restaurant. Suffice it to say we didn't starve, but her so-called language ability was the stuff of hyperbole.

You'll do better - much better.

1 Like

Wordsmitty ✍️

Sep 14, 2024 at 1:11pm
In response to "One Thing In Common"

Pictures! We'll need to have pictures. No, not of you, not of buildings or countryside. Hevans NO. Don't take pictures of people. Need the important stuff - of the Beer. It'll also be a good record when you get back and are missing a few days here and there.

2 Like

Robert Waltz

Sep 14, 2024 at 10:40am
In response to "One Thing In Common"

WakeUpAndLive️~Happiness

- from that article, Travel expert Samantha Brown added that, sometimes, hotels will provide only one small towel. She thinks there’s a case to be made for bringing a small sports towel on your travels, just in case.

As everyone who's familiar with The Hitchhiker's Guide to the Galaxy knows, one should always carry a towel.

1 Like

WakeUpAndLive️~Happiness

Sep 14, 2024 at 10:31am
In response to "One Thing In Common"

https://www.washingtonpost.com/travel/tips/europe-travel-etiquette-tipping-ameri...

1 Like

WakeUpAndLive️~Happiness

Sep 14, 2024 at 10:19am
In response to "One Thing In Common"

No worries, English will do in Europe in most countries. How exciting it's near your travel date. Still, more than 5x24 hours to go. Take it easy. It should all be fun.

1 Like

Robert Waltz

Sep 13, 2024 at 5:57pm
In response to "Journey Man"

You two are both exceptional individuals, it's true.

1 Like

Annette in Paris

Sep 13, 2024 at 4:29pm
In response to "Journey Man"

As long as there's beer, it's possible to have fun with you for a whole week.

Ken, get your head out of the gutter. I'm talking about visiting micro breweries.

1 Like

Sum1's In San Francisco

Sep 13, 2024 at 4:19pm
In response to "Journey Man"

From your post. Since it's a documented fact that no one can put up with me for more than two hours at a time, I tend to do road trips alone. Hey, I 'put up' with you for a whole day! Or was it the other way around?

1 Like

Aiva Raine

Sep 11, 2024 at 3:36pm
In response to "Drop and Gimme Twenty"

Happy 20th. We're glad you joined and doubly glad you've stayed this long. I look forward to reading your daily blog as part of my own daily ritual.

1 Like

September 11, 2024 at 11:48am

#1076615

Drop and Gimme Twenty

Somewhat predictably, I'll take a break from the usual today in order to blab about this being my 20-year anniversary here.

Unfortunately, I said most of what I wanted to say back on September 1, as we began the site's 24th anniversary: "Four and Twenty"

Having my own milestone so soon after that of the website itself, though, is kind of like I'd imagine it would feel like for your birthday to be on December 26: everyone's burned out on celebrating, including me. Especially me.

Which is fine. I'm on board with celebrating actual birthdays, but membership anniversaries are just, well, whatever. Still, this being the 20th, one of those nice rounded-end numbers, I felt I should say something about it.

Things were a bit different back in 2004. Smartphones weren't ubiquitous yet. The internet hadn't become a mire of scams, ads, and influenzas. And a certain other event that took place on a September 11 was still fresh on everyone's mind.

I hadn't intended to join on the 11th, for that reason. I tried to create an account here the previous day (my dad's birthday, and he was still alive back then, so already a significant day for me), but for whatever technical reason, it never took. That's also how my username got the annoying 02 at the end; while the account didn't work, my attempt was enough to block off just "cathartes" as already in use. It's been long enough that I don't remember all the details exactly (hell, 20 days is probably long enough for that, for me), but I vaguely recall creating this account with help from a friend who was already a member, shortly after midnight, forcing my account anniversary to be on a day that was already infamous.

I've considered changing my username to something else, but never went through with it. It's kind of part of my identity now, so I'm ambivalent about the idea.

So, I'll just finish by posting what I'm pretty sure was my first item on here, created on September 11, 2004—but which I'd written some years earlier: "Ghost Poem #1"

[ASR]

Odd that it was a poem, I suppose, because I'm more of a fiction writer and, now, a blogger, but I suppose it was something quick and simple to put up here to get started. And even back then, when I had an actual job and a spouse, I was all about quick and simple.

Some things don't change all that much.

6 Like • Comment • View 4 comments

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