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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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And again from "JAFBG"  [XGC]:What widely-accepted piece of advice is actually total bullshit? Whoa. Like, where to begin? I suppose "Don't get that vaccine, just eat horse dewormer if you get sick" would be too obvious. But it fits the prompt. Perhaps something a little more general, like "Be yourself?" No, that one isn't total bullshit -- if you're attractive, rich and charming. If you're not, "be attractive, rich and charming" would be better advice. If only there were some way to successfully follow it. Oh, I know one! "When you get to prison, find the biggest inmate and punch them in the face to establish dominance." Yeah -- that's not great advice unless you want to avoid your long prison sentence by being dead. But it also won't apply to most people. Let's see... "Put all your cash into cryptocurrency?" Nah, not widely-accepted enough to qualify. But total bullshit. Well, I suppose if you like to gamble. But I like to gamble and I still stay away from that nonsense. So I'll dig deep, go against the grain, and follow several other clichés to suggest that one widely-accepted piece of advice that is total bullshit is... Never give up. A couple of years ago, there was a guy out in the desert who was absolutely, totally convinced that the Earth was flat, and that anyone who said otherwise was part of a vast, overarching, global (snort) conspiracy. What he believed the purpose of the conspiracy was, if anything, I don't really know, but it's irrelevant. So he built a rocket. I guess because the rockets that other people built and used to orbit the really very obviously round Earth were all part of this grand conspiracy or something. In case you've forgotten this little incident, here's the report of his final flight , which failed to prove or disprove the planar nature of the planet, but did effectively provide further evidence to support the theory of gravity."Mad" Mike Hughes, 64, crash-landed his steam-powered rocket shortly after take-off near Barstow on Saturday. 1. Appropriate nickname. 2. Steam-powered rocket. 3. I can't emphasize this enough: steam-powered rocket. A video on social media shows a rocket being fired into the sky before plummeting to the ground nearby. You know, as mulishly ignorant as this guy is, I don't want you to get the impression I'm amused by or celebrating his death. Nor do I have any interest in viewing a snuff video. But I will admit to making "not exactly a rocket scientist" jokes. At least when Musk played with rockets that demonstrated lithobraking, they weren't crewed. Hughes was well-known for his belief that the Earth was flat. He hoped to prove his theory by going to space. 4. Again... other people have done this and reported extensively on it. Complete with photographic evidence. 5. Moreover, one does not need to go into space to demonstrate the curved nature of the surface of the planet. 6. Specifically, we've known this since at least 500 BCE, thanks to math. You know, the stuff you need to know to do rocket science. With the help of his partner Waldo Stakes, Hughes was trying to reach an altitude of 5,000ft (1,525m) while riding his steam-powered rocket, according to Space.com. 7. 5000 feet? 8. I will remind you that he did this in or near Barstow, California. 9. Barstow is approximately 140 miles from the highest mountain peak in the continental US. 10. Said mountain (Mt. Whitney) has a summit approximately 14,500 feet above sea level. 11. Therefore, he could have fucking climbed Mt. Whitney and exceeded his goal altitude by a factor of nearly 3. 12. Or gotten into a jet that would cruise at around 30,000 feet. 13. And that still wouldn't have been enough to convince him. My point in going through all this is not to make fun of idiots or the stubbornly and willfully ignorant, though I'm certainly not above doing so. No, my point is that if he'd believed and listened to actual science, Hughes might well have given up. And possibly still be alive today. Except he probably wouldn't be, because I guarantee you he'd also deny the existence or severity of COVID, and was old enough to get hit hard by it. Had he lived, though, I don't know, maybe Bezos could have given him a ride in that giant phallus of his. I'd have loved to hear what he had to say about it afterward. My guess, though? For people like that, no amount of evidence would be enough, and he'd have found a way to double down on the flat-earth assertion. The moral of this story is: It's great to have a dream. It's great to pursue it. But at some point, if people keep telling you that it is not possible for a human to breathe water, you can either give up on proving it for yourself by sticking your head in a bucket, or you can die drowning. Yes, there have been instances in history of people who insisted that they were right, while the established beliefs were wrong. But in nearly every one of those instances, it was a matter of scientists doing science and pushing back against ignorance and superstition. Hughes was doing precisely the opposite of this. Want to know how to spot a crackpot? See if they say something like "No one believed Galileo either!" If they do, back away slowly. In other words... give up. |
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