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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 can't for any amount of money recall why I saved this particular Cracked article, but I'm going to link it anyway. History is full of success stories. These are not those. The idea that you need to “strike while the iron is hot” has morphed from a straightforward explanation of blacksmithing into an endlessly repeated cliche. It, or some more unwieldy modern rejiggering, is plastered over everything from horoscopes to aviator stock photos on hustle culture Instagram accounts. Every cliché was once profound wisdom. Plenty of people throughout history have filled their metaphorical blade with microfractures by waiting too long, while others have snapped the sword in half entirely because of ill-advised hesitation — losing a couple million dollars or an entire city in the process. It's not enough to invent something; one must also have the imagination to see the implications in one's invention. 5. Greeks Almost Inventing The Steam Engine Eh. This one wouldn't have gotten very far, anyway. The math wouldn't be ready, also the fault of the Greeks, who insisted that irrational numbers were of the devil. 4. Not Signing The Beatles This is fairly well-known, I think, and usually held up as an example of big mistakes. Now, Decca Records weathered the blunder and has still been plenty successful in their own right. I think maybe I had in mind, when I saved this article to my queue, something like "just because a publisher rejected your manuscript doesn't mean it sucks." However, it still might. It's just not a sure thing. 3. Passing on the Patent for the Telephone Orton and Western Union were offered the patent to a newfangled communication device invented by Alexander Graham Bell, one we know as “the telephone.” Sure, the asking price was high at $100,000, but you’d like to think the head of a communications company might see the value in the fucking telephone. Instead, he balked, apparently not seeing a future in the device that would, you know, literally define the future. This is where that lack of vision comes in. Western Union was used to doing business a certain way, and the telephone would have changed that. See also: Sears, who could have seen this whole Internet coming and positioned itself to take advantage of it, but no, Amazon won that race. 2. The Byzantine Empire Not Buying A Huge Cannon In general (pun absolutely intended), if you're at war, don't turn down enemy-destroying weapons. 1. Not Letting Hitler Drown By contrast to some earlier entries, this one's not a lack of vision. I'd like to think most of us would save a drowning kid, if we had the opportunity and didn't know for sure he'd grow up to be a genocidal autocrat. In 1894 in Germany, a man named Johann Kuehberger saw a drowning boy in a river and, without a second thought, strode in to save his life. Incredible, awe-inspiring, medals all around, right? At the time, sure. Time-travelers, take note: this is your moment. Except killing baby Hitler is the biggest cliché in time-travel fiction, and we don't know if the result would have been worse. "But what could be worse than 11 million dead people?" Well, someone just as evil and actually competent might have risen to power, someone who wouldn't have done the 20th century equivalent of turning down a war-ending cannon by losing all their rocket scientists and nuclear engineers. |
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