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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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Another entry for "Journalistic Intentions"  [18+], this one about a trope.The Random Number Generator (peace be unto it) is messing with me again. I just did a "woman in a non-traditional role" entry yesterday. Fortunately, this one's about a trope in fiction. Unfortunately, it's sometimes difficult to talk about the fictional trope without referencing those works of fiction that purport to be biographical. Let's start with the TVTropes page. Fair warning: the page suffers from grammar issues. But I think it gets the point across. For most of mankind's history, leadership and authority are associated with men. We could start by not calling humanity "mankind." After all, a leader — especially the supreme ruler of a nation — are expected to be strong (to defend their borders), ambitious (to expand and improve their territory) and aloof (so that they won't be swayed from their long-term goals by a moment of impulse), all of which are often considered masculine qualities. And yet, some of the greatest rulers in history have been women, and some of the worst have been men. To be fair, there are far more examples of the latter. Perhaps the male ones didn't have to do quite as much to prove themselves capable leaders, due to expectations. Again, though, we're talking about fiction here, and we can write our queens however we like. So when a woman finds herself in a position of power, expect her subjects to be less than enthused by the idea — a volatile, emotionally-driven, Hysterical Woman in charge of other? You know who lets emotions get in the way of ruling? Men. Well, anyone, really. We're all human. Society expects us to demonstrate our emotions differently, but in all cases they sneak through sometimes. While it is possible for this trope to apply to male rulers (if the man in question lacks the traditional masculine qualities, or if the work is set in a Lady Land and the man is forced to be more "feminine" to be accepted), what makes this an Always Female trope is the still commonly held view that leadership is an inherently masculine role, and the point of the trope is that the character suffers emotionally because they are forced to divest themselves of their society's gender norms just to be taken seriously as a monarch. An ardent feminist once asserted to me that the world would be a better place if all its leaders were women. While I don't really have an argument against that, just to be a troll, I said, "Margaret Thatcher." She responded with, "She doesn't count!" And now I have an even better counterargument. The UK Prime Minister isn't, however, a royal; women who are elected (even indirectly, in that case) aren't really part of this trope. Still, I suspect that any hereditary ruler who isn't a sociopath to begin with has to wear a mask of some sort, regardless of sex or gender identity. Even in an absolute monarchy, rulers are expected to abide by certain... well, rules. And if they don't, if they let sentimentality or passing emotions guide them, well, they tend to get stabbed in the back. Sometimes literally. I don't think that's any easier for men than it is for women, but I have no way of knowing. One of the purposes of fiction is aspirational; it doesn't always reflect reality, but rather display how the writer thinks reality should be. And we get used to whatever it is they're portraying. The more shows depict a competent female President, for example, the more likely we are to have one. Not only do we get used to it, but maybe it becomes a bit of an ideal to strive toward for the real person who eventually gets that position. |
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