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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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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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June's almost over -- it seems so short and yet interminable at the same time -- and next month I'll be in "30-Day Blogging Challenge ON HIATUS"  [13+] again.So, today, I'll talk about one of the reasons most of us are here: words. https://www.mentalfloss.com/article/51150/12-old-words-survived-getting-fossiliz... 12 Old Words That Survived by Getting Fossilized in Idioms Not going to repeat all 12 words here, just some highlights. And then it'll be your turn, for a chance to win a Merit Badge. English has changed a lot in the last several hundred years, and there are many words once used that we would no longer recognize today. For whatever reason, we started pronouncing them differently, or stopped using them entirely, and they became obsolete. I'm pretty sure I've talked about things like that before. I know I have a couple more in the queue, though it'll probably be at least August before I get to them. There are some old words, however, that are nearly obsolete, but we still recognize them because they were lucky enough to get stuck in set phrases that have lasted across the centuries. We writers like to deride clichés, and usually for good reason. But we tend to forget that almost every trite phrase was once poetic and meaningful. 1. Wend This, to me, is one of the more interesting ones because of the history: The past tense of wend was went and the past tense of go was gaed. People used both until the 15th century, when go became the preferred verb, except in the past tense where went hung on, leaving us with an outrageously irregular verb. In case you were ever wondering why English has such different words for present and past tense of "go." 7. Fro The fro in "to and fro" is a fossilized remnant of a Northern English or Scottish way of pronouncing from. This one is probably obvious, or at least it was to me when I first encountered it. But it never made sense. I mean, if the o sounds at least rhymed, I could see it, but no, we get an oo sound and then an oh sound. They're only related because they happen to be represented by the same letter. "to and fro" makes precisely as much sense as "to and from." But at least there's historical reason for it, as this list demonstrates. 12. Shrift We might not know what a shrift is anymore, but we know we don't want to get a short one. Shrift was a word for a confession, something it seems we might want to keep short, or a penance imposed by a priest, something we would definitely want to keep short. But the phrase "short shrift" came from the practice of allowing a little time for the condemned to make a confession before being executed. Unlike #7 there, this one made some sense to keep around. No, it doesn't rhyme, but it has that nice double alliteration: short shrift.  So, mini-contest time! Take a look at the full article at the link (it's short). Do you have a favorite word or expression (other than the ones at the link) that involves a rare or otherwise obsolete word? I'm sure there have to be others besides the twelve listed. And if coming up with one stresses your brain too much -- it does mine; I'm not coming up with any, myself -- then I'll accept any word (or phrase) with an interesting history. Just keep it real; I'll (hopefully) be able to sniff out faux or folk etymologies. The one I like best will earn the commenter a Merit Badge. This could be because it's funny, or interesting, or both. As usual, deadline's midnight WDC time, and please leave the comment here and not in the Newsfeed. |
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