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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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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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| I did a thing yesterday that I've never done before. It's not much of an accomplishment, really. And I didn't exactly set out to do it. It was only toward the end of the experience that I said to myself (and my passenger): "Huh. In all of my half-century plus of visiting New York, I've never done that before." Also, in fairness, it's very easy to do something in New York that you've never done before. It would take more than a lifetime to do everything in this city, after which there would be a whole buttload of new things to do. Kind of like my life goal of visiting every brewery. Anyway, after that buildup, the thing that I did seems even more anticlimactic, even trivial, but I'm going to tell you anyway: in one afternoon, I visited all five boroughs of the city. Starting in Staten Island, I drove over the Verrazano into Brooklyn, around the Belt Parkway into Queens, stopped at my mother's grave just outside the city on Long Island, then crossed over into the Bronx and thence into Manhattan. I'm told that one can accomplish this feat on foot by participating in the New York Marathon. Hahahahahaha no. Besides, it would take me more than one afternoon to runcrawl the marathon. More like a week. There are myriad other ways to do it, too. One interesting routing problem would be to develop a route, whether walking, driving, biking, or public transportationing, of minimum distance while still touching ground in all five boroughs. My route wasn't in any way efficient; it was mostly just a result of getting from New Jersey to the cemetery and then to Manhattan. It's not an accomplishment at all, just a fun bit of trivia. Want to impress someone? Visit all 50 US states in one day. Sounds difficult, but I'll bet someone with a private jet and lots of money could find a way, and probably get all kinds of publicity for it. Me, I once drove all the way from the easternmost point to the westernmost point of the Continental US (walking the last steps between road and coast), which I thought was a bit of an accomplishment even though I purposely took my time, but no one put me on the news for it. And hell, I haven't visited all 50 states yet. Alaska, Nebraska, and Michigan are still on my list, though never in winter. |
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