Complex Numbers (Book)

Blog Calendar

◄ January ►
S	M	T	W	T	F	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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 4 hours ago
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

about 4 hours ago
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

about 4 hours ago
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!

about 4 hours ago
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!

a day ago
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

a day ago
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.

Sum1's Home!

a day ago
In response to "Cell Mates"

@Jayne

Should I Play Grammer Police here, and tell you that you misspelled Henlein? He's one of my favorite authors. If I had the money (I do really), and a place to keep them (I don't), I would get his entire collection from the Heinlein Society. I have read many of his books and short stories, there are also many that I haven't read too.

1 Like

🌖 HuntersMoon

a day ago
In response to "Cell Mates"

Sum1's Home! / Jayne - You make me feel like a stranger in a strange land.

2 Like

Jayne

Jan 10, 2025 at 2:02pm
In response to "Cell Mates"

I'm charging you 85 gps for making me think of Heinlen. Feel free to ignore the invoice, my molecular makeup is too unorganized to develop a collections department

4 Like

Sum1's Home!

Jan 10, 2025 at 1:38pm
In response to "Cell Mates"

One word in your post made me smile, and ask this question to myself. How many people will understand the word 'Grok', and where it originally came from? I must have read that book 2-3 times before I really grasped its meaning.

3 Like

January 12, 2025 at 9:31am

#1082271

Revisited: "Squash Court"

Today, being a Sunday, is Time Travel Day. Back near Halloween of 2021, I wrote an entry about squash and its botanical relatives: "Squash Court"

The more I learn about squash and its relatives, the less I know. That's a bit of a cliché, but it describes my confusion fairly accurately. It's not like the cabbage cultivars, also mentioned in that entry, which are varied but somewhat limited. In contrast, there's a dizzying variety of gourdlike berries, and even calling them "berries," while apparently correct by botanical definiton, only adds to the confusion. Some are edible. Some are not. Many of the hardier ones are used as decoration, including the always-popular pumpkin.

Funny thing about pumpkins. They're all over the place in the fall, which is the season when I wrote that entry. Then they disappear for like 9 months, only to reappear again the following September, along with their associated spices and, largely unrelated but important, Oktoberfest beer.

It's not like we have to eat seasonally. One of the few things keeping us from sliding into full-blown dystopia is being able to eat pretty much everything year-round, including stuff from halfway around the world. Some people object to this availability. I do not. And yet, here in the middle of blasted winter, I'd completely forgotten about the existence of pumpkins until my random number generator pointed me to that entry.

Sure, it's understandable, as they're a major symbol of fall, at least in my part of the world. But, for instance, zucchini (related to squash) is most definitely a summer vegetable—using the culinary definition now—but they're available year-round. Which makes them harder for me to avoid. Yes, I've gotten over my dislike of zucchini, as noted in the linked entry, but that doesn't mean I go seeking them out.

The availability of the actual prompt for that entry, the delicata squash, I still don't know, and I'm not sure I've ever seen it in grocery stores or restaurant menus.

One thing I neglected to do back then was look into the etymology of "squash." As a kid, I always figured it was related, somehow, to the verb. Like you're supposed to squash the stuff like you mash potatoes. This annoyed my mother, but that was just a bonus for me; it was easier to pick up bits of squashed squash and eat it with the almost-edible other stuff on my plate. So I never gave it much thought. Until now.

Turns out the word squash, used for the food, is completely unrelated to the other definitions of squash (the verb or the ball game) and is, at least according to one source, from the Narragansett word asquutasquash. English people being English, that became squash. Presumably, other Native peoples had different names for it, but I can't be arsed to look up all of them.

So there it is: a long-standing mystery to me, finally resolved. Now if I could just figure out all the phylogenic tangle for all their many and various relatives, I might feel a sense of accomplishment.

4 Like • Comment • View 4 comments

© Copyright 2025 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.