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Thursday, Jan. 16, 2025

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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:

tj is ready for spring!

about 21 hours ago
In response to "Walk the Prank"

If a practical joke backfires is it an impractical joke?

2 Like

tj is ready for spring!

a day ago
In response to "Failure Is Victory"

Just think, back in the mid seventeen hundreds, Ole Ben had himself an electric BBQ; he stunned the turkey, shocked himself and cooked the bird on a gadget called an electric jack. Personally, I think he should have used a pellet smoker.

2 Like

🌖 HuntersMoon

a day ago
In response to "Failure Is Victory"

"Yes, even I make mistakes sometimes."

You may remember, that once words are placed on the internet, they last forever. They WILL come back to haunt you.

3 Like

tj is ready for spring!

Jan 13, 2025 at 12:55pm
In response to "Rebel Without a Clause"

It's just like this sometimes.

1 Like

🌖 HuntersMoon

Jan 12, 2025 at 9:58am
In response to "Revisited: "Squash Court""

tj is ready for spring!/Robert Waltz

Oh My God!

Now I understand the etymology of "Pun-ishment."

3 Like

Elisa: Snowman Stik

Jan 12, 2025 at 9:44am
In response to "Revisited: "Squash Court""

Ironically I'm eating scrambled eggs with zucchini as I read this entry.

As someone who has shopped for and cooked delicata squash, I can say that they're mostly seasonal. I occasionally see them in the summer, but they're far easier to locate in the cooler months. They haven't quite broken out the way zucchini has or even acorn squash. I can find acorn squash year round, although admittedly I don't eat it in the warmer months. Speaking of which, if I had to guess, I think pumpkins aren't sold year round because A. summer demand and applicability is low and B. size is a factor. Acorn squash is grown in similar areas/conditions as pumpkin, but it's a smaller size. Grocery stores can carry it year round in a smaller footprint compared to pumpkin even if fewer people are buying it in the warmer months.

4 Like

Robert Waltz

Jan 12, 2025 at 9:41am
In response to "Revisited: "Squash Court""

tj is ready for spring!

- if he has lesser relatives in the produce section, that must be why he's called Bigfood.

4 Like

tj is ready for spring!

Jan 12, 2025 at 9:38am
In response to "Revisited: "Squash Court""

Here in the north woods there are rumors of a giant squash that roams the woods; Sasquash! I've never seen him, but do, on occasion, come upon his lesser relatives in the produce section.

4 Like

tj is ready for spring!

Jan 11, 2025 at 12:48pm
In response to "Time Marses On"

I agree. When we finally get close to inhabiting Mars, I doubt anyone will be scouring through sci-fi books to find a design, asking, "How 'bout this, it looks pretty cool."

1 Like

Robert Waltz

Jan 10, 2025 at 4:24pm
In response to "Cell Mates"

Oooh, a demonstration of Waltz's First Law of the Internet: Any post criticizing someone's grammar, spelling, and/or punctuation will itself contain grammar, spelling, and/or punctuation errors.

I'm pretty sure I've read all of Heinlein's books and stories, with the exception of the naked money grabs his estate published posthumously. Some of them didn't age well, but taken in the context of their time, many of them are solid science fiction.

And I can't tell you how many times I've wanted to use "grok" in an entry but passed because I didn't want to overuse it. As the blog is nearing its end, I threw caution to the wind today.

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