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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 Best Blog in the 2021 edition of [Link To Item #quills] !](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quill_Award-1375927_6.gif) ![Merit Badge in Quill Award 2
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2022 Quill Award - Best Blog - [Link To Item #1196512] . Congratulations!!!](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quill_Award_2-1375927_6.gif) ![Merit Badge in 30DBC Winner
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Congratulations on winning the Jan. 2019 [Link To Item #30dbc] !!](https://images.Writing.Com/imgs/writing.com/writers/badges/group-30DBC_Winner-2064535_14.gif) ![Merit Badge in Blogging
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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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I highly recommend your blog.](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-Highly_Recommended.gif) ![Merit Badge in Opinion
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For diving into the prompts for Journalistic Intentions- thanks for joining the fun!](https://images.Writing.Com/imgs/writing.com/writers/badges/genre-Opinion-1150.gif) ![Merit Badge in High Five
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For your inventive entries in [Link To Item #2213121] ! Thanks for the great read!](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-High_Five.gif) ![Merit Badge in Enlightening
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For winning 3rd Place in [Link To Item #2213121] . Congratulations!](https://images.Writing.Com/imgs/writing.com/writers/badges/general-Enlightening.gif) ![Merit Badge in Quarks Bar
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For your awesome Klingon Bloodwine recipe from [Link to Book Entry #1016079] that deserves to be on the topmost shelf at Quark's.](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quarks_Bar-2046190_12.gif)       |
| On December 14, 2019, I wrote a blog entry. It wasn't a big deal at the time, just my default: commentary on something I found on the internet. What I didn't know, didn't plan on at the time, was that it would be the first in what is, as of today, a three-year streak of daily blog entries. I also couldn't have known that, a mere three months later, shit would change because of a global pandemic. I almost certainly wouldn't have this streak if it weren't for that; I had travel plans. In truth, I'd rather have been able to do the travel plans. I still want to visit Belgium, dammit. It's been put off due to travel restrictions, crappy airline service, and World War III. To that end, I have another streak going: over 1200 days on Duolingo. Which, if you do the math, is longer than my daily blog entry streak. I'm very close to being done with the French course, which absolutely doesn't mean I'm fluent in French, though I certainly know more than I did three years ago. I might try Dutch again. Learning two languages at once proved difficult for me, and Dutch is similar enough to English to confuse me. But it's one of the other languages they speak in Belgium. Yeah, I know, lots of people speak English there as well, but this way I might have some idea if someone's insulting me in a different language. My progress is slow, I know. But that's what I get for waiting until my 50s to try to learn something new. Lots of people my age don't even bother. At least I found out that I could do something daily. About the only thing I could do on a daily basis, before this, is breathe. Even eating didn't happen every day. The breathing thing was questionable there for a while, too, but I managed to keep doing it. So, am I going to keep the streak going? Well, I'm not going to deliberately break it at this point. If I do manage to go abroad, I might not have the means. I'll be okay with that, because at least I'll be traveling. Then there's always the chance of the unexpected: no internet access, computer craps out, I get injured or get sick or die, that sort of thing. You'll know that one of those happened because I won't announce it in here beforehand. Tomorrow I'll have another article to comment on, but today I just wanted to reflect on what is, to me, a mighty achievement. |
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