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Monday, Nov. 18, 2024

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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 ✍️

about 2 hours ago
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

2 Like

Brandiwyn🎶

about 4 hours ago
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

Brandiwyn🎶

about 4 hours ago
In response to "Losing Weight Is Easy"

Has anyone ever told you how annoyingly pedantic you are?

Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless.

2 Like

tj-turkey-jobble-jobble-hard-J

about 23 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

Nov 16, 2024 at 9:24am
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

March 20, 2023 at 9:48am

#1046731

Scorn on the Cob

Spring begins today! My local weather celebrates the occasion by being colder than it's been for a month.

Speaking of annoyances, another prompt from "JAFBG"

[XGC] today...

Share one 'hard limit' that would make you walk away from a relationship or friendship. Has that limit changed over time?

Let me answer the question before obeying the directive:

Yes. Yes, it has. And you might think that, as I get older and more desperate (in theory) for the kind of human connection that is denied to me due to my looks and personality, that I'd relax my standards a bit, but nothing could be further from the truth: I find I put up with less and less bullshit from people.

There are plenty of things I'll put up with in a friend, though, that I wouldn't want to deal with in a more intimate relationship. Veganism, or some other eating disorder, for example. If it's a friend, it doesn't affect me; eat what you want (if you try to claim moral high ground for it, though, we'll have a problem). But I'm not going to eat penance food, nor am I going to stop cooking meat-based dishes. Also, I'm pretty proud of my cooking, and would want to share it. The point being that it wouldn't make me any less a friend to someone, but that's all we'd be: friends.

So we need a dealbreaker that works for all kinds of relationships, and picking one is pretty obvious:

Being rude to service workers.

Now, obviously, all of us have bad days, sometimes. I'm not talking about the occasional snap. I mean a repeated pattern of treating cleaners, servers, receptionists, baristas, cashiers, bartenders, etc. (especially bartenders) like The Help.

Whether conscious or not, this kind of behavior is reflective of a hierarchical attitude: "some people are beneath me in social status and can be safely scorned; others are above me and must be appeased." So that's what I watch out for in potential friends: how they treat those of perceived lower social status.

And no, this doesn't lead to a virtue paradox: I don't think that rude people are beneath me; I just don't hang out with them if I can avoid it.

4 Like • Comment • View 4 comments

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