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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.




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February 5, 2023 at 12:01am
February 5, 2023 at 12:01am
#1044278
Today's historical document comes from just shy of 14 years ago. It was part of a series of entries that I did to expand on a list of things about me. I mean, it's a blog; why wouldn't I talk about me?

Anyway, this particular entry is here: "Lassie" Open in new Window.

From that day:

11. When I was a kid, I had a collie named Lassie. Yes, I named her. Give me a break; I was four years old at the time.

Incidentally, I've never used her name as a security answer anywhere, so... nice try, but no.

I've posted this before, but here's a picture of me with Lassie, from the rotation in my former blog:

Unlike many pictures, I could easily repost it here. But why, when I spent so much time typing in the link to the entry?

I don't know how old I was in the picture. Over four, obviously. I suck at estimating ages of kids or adults. No, it's irrelevant that the picture is of me. It was ancient when I put it in that entry. And after another 14 years, I'm even further removed from that brat, and even more embarrassed by the photo.

It occurs to me that I don't even recall the circumstances surrounding the photo. That's not our lawn. I don't recognize the setting at all. I have this vague notion that it might have been Florida, but I have no recollection of taking the dog with us to Florida. Or even who watched her when we vacationed.

I only keep it up because of the dog. She was a good dog.

I've never had another dog. Most of them annoy me, and those that don't, already belong to someone else.

That's not the main reason. Oh, it might have been in the forefront on that day, for that entry, but I rarely have only one reason for doing (or in this case, not doing) something. I like dogs, mostly. I just can't be arsed to do the work they require.

And also because I doubt I'd find one as cool as Lassie.


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