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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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June 9, 2024 at 8:44am
June 9, 2024 at 8:44am
#1072376
Delving into the depths of the past once again, the random numbers landed me on this origin story of sorts, from all the way back in 2008: "Housekeeping" Open in new Window.

On my computer at work, I have a Favorites folder called "Blog Fodder."

Fortunately, I no longer waste time at work, and my Blog Fodder list resides on my laptop. Nowadays, of course, these things are portable between devices, just when that feature became nearly useless to me.

Into it I drop the random links people send me, some of which end up here.

Every once in a while, someone will still send me a link, and I usually appreciate it. But I find most of my material from other sources. No, not social media, which I generally shun.

But there's usually more links than I want to blog about, or maybe some of them fit a theme while others don't.

Obviously, I ended up resolving this non-issue by picking just one at random when it's blogging time.

The rest of that entry was me cleaning house (hence the entry title) by dumping three links with brief quotes and commentary.

I won't bother rehashing that bit. The links are, remarkably, all still active as of right now, but being older and dumber now, I don't think I find them as amusing as I did 16 years ago.

And it's not really an origin story; apparently, I'd been commenting on links for a while even then. But that might have been the first time I explained anything about my process.


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