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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif) ![Merit Badge in Highly Recommended
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| Some prompts, I just have a hard time relating to. PROMPT September 18th When you have an unexpected hour of free time, how do you fill it? Sleep. At least, that would have been one of my answers back when free time was a precious commodity for me. The other answer, on those ultra-rare occasions when I wasn't dead tired, was reading. Seeing this prompt, though, reminded me of how great it feels to not have pressing obligations all the time. It was like my chest was constantly in a vise, and when I retired, those clamps finally loosened up. I had so much going on, so many things I had to do and things I wanted to do but couldn't bear to go without, so something had to give, and that something was sleep. So when I got a chance, sleep was my preferred recreational and restorative activity. Still is, really. It's magical: you need to make time pass, so you fall asleep and then suddenly, boom, it's time to do... whatever it is you needed to do. I've heard some people say that they wish they didn't have to sleep. Think of all the things you could get done! More time to be productive! More opportunity to serve your masters! Don't you want to do more, more, more?! No, thanks. Anyway, this sort of thing doesn't apply to me now. I do exactly what I want to do most of the time, so as far as I'm concerned, it's all free time -- visits to dentists and whatnot notwithstanding. Though I could argue that while I, like most people, dislike trips to the dentist, I dislike tooth problems more, so I want to do that, too. I've got one of those coming up in a couple of weeks. Root canal. Not my first root-io, either, so I know the drill. (Yes, that's a pun.) It's not painful like you hear about; it's more... well, they numb you thoroughly and you're sitting in a dentist chair for two hours while they do unspeakable things to the insides of your tooth, and the occasional tiny wisp of smoke drifts from your wide-open mouth across your field of vision. Even that wouldn't be so bad if you didn't occasionally smell it. So even if you wanted to, you couldn't actually sleep through it. But it's incredibly, mind-twistingly boring. (You can consider that a pun, too, if you want.) That's the worst part of it. You're sitting still for a couple of hours and you can't do anything, not sleep, not talk, not read, not watch a movie, not play a game... just stare at the ceiling and try not to think of what's really happening to the once-living tissue inside of your tooth. I mean, I'm sure it's no picnic for the dentist or her assistants, but at least they can think about the BMW they can buy with what you're paying them. I expect they don't put you completely out because there's no real reason to, and there's always a risk with general anesthetic. But you'd think at least, by now, they'd have it so you could put on some kind of VR headset and watch Little Shop of Horrors during the whole ordeal. Okay, maybe that's a bad choice of movie. Still. Afterward, I won't be able to eat or drink anything for a while, so I'll do the one thing that I know will make the time pass until the anesthetic wears off: Sleep. |
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Finally. Fascinating stuff. All of them. There is something rather philosophical about comedy. You are certainly right there. 
