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Thursday, Nov. 21, 2024

2:25pm EST

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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:

Robert Waltz

about 24 hours ago
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

about 24 hours ago
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

a day ago
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

a day ago
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
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.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
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🎶

Nov 18, 2024 at 11:19am
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.

3 Like

tj-turkey-jobble-jobble-hard-J

Nov 17, 2024 at 4:04pm
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

October 20, 2024 at 9:02am

#1078619

Revisited: "Unlucky"

Going back over 5 years, today's peek into the past takes us to an entry from July of 2019: "Unlucky"

I've written about luck several times in here, but this entry isn't directly about that; it's a play on the word "potluck." The entry is a response to a prompt, most likely from 30DBC: "What is your go-to dish to bring to a potluck? Does your family have any traditional recipes? (In Hawaii, these appetizers are called 'pupus'"

What I apparently didn't catch at the time was the reference to appetizers; in mainland North America, a potluck is when you bring a dish of any sort to a communal gathering. The dish could be an appetizer, but it could also be a main course (my entry goes on about casseroles for a good bit) or a dessert.

Casseroles, however, mystify me. I'm not sure why. They can't be that hard to do, or millions of Southern Baptists wouldn't do them, in all their various incarnations. You'd think that would teach them something about variety and the wonders of diversity, but... no. They just plop down their armies of Corningware, oblivious to the obvious metaphor.

Since then, I've tried my hand at various casseroles, with a good bit of success. They're less work than other dishes, but still harder than, say, popping a frozen thing into a microwave.

But what stumps me is that I don't know what the essential thing is that makes a casserole a casserole and not something else. Baking? You also bake lasagna; is that a casserole? Meat? Nonsense; there are plenty of vegetarian casseroles.

I've also had several entries about classification problems, like my perennial assertion that a hot dog is not a sandwich, but a taco.

So, yeah, no traditional family recipes here. Just stuff I've picked up along the road.

As I noted in that entry, if there were traditional recipes in my family, they'd be borderline inedible, and I'd have no problem letting them fade away.

Fortunately, one of the comments helped me to clarify the "what exactly makes a casserole a casserole" conundrum. I occasionally get comments here that thank me for helping the commenter learn something new, but I assure you, that works both ways.

Just lucky, I guess.

4 Like • Comment • View 3 comments

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