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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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| Today in the US is Martin Luther King Day, a federal holiday celebrating the Reverend Martin Luther King Jr., a civil rights activist best known for advancing civil rights through nonviolence and civil disobedience. In August of 1953, King delivered his famous speech “I Have a Dream” calling for civil and economic equality for all Americans and the end of racism. On this Motivational Monday, write a speech advocating for something you’re passionate about and use the phrase “I have a dream” in your entry. We need space. We need space, not because going there will solve all of our problems, but because it is there. We need space, because we're only insignificant if we allow ourselves to be. Fifty years ago this year, humans walked on the Moon for the first time. As I write this, that Moon is eclipsed. Our satellite slipped into our shadow and darkened. During a lunar eclipse, the Moon glows red. That red is sunlight, scattered by the atmosphere. If we could stand on the Moon right now, the Earth would be a huge red ring in the dark sky, the light of every sunrise, every sunset, every twilight illuminating the lunar orb. Some say we shouldn't bother with space, that we should solve our problems here, first. Well, we've had fifty years to solve our problems, and we still have problems. We shouldn't go to space, they say, because there's still poverty, still hunger, still war, still crime. But do we stop searching for a cure for pneumonia just because we haven't found a way to end cancer? Do we stop convicting rapists because there are murderers out there? Do we stop feeding ourselves because someone else is still hungry? There are over seven billion of us. I think we can work on more than one thing at a time. Do you think it's a waste of money? Why? Are you under the impression that we stuff dollar bills into rockets and blast them into orbit, never to be seen again? No. That money enriches our economy. It helps all of us, rich and poor alike. The things we've already learned have improved our quality of life immeasurably. And there's still much more to learn. Everything we learn helps us to prosper. Everything we find advances science. Is it difficult? Yes. Is it dangerous? Oh, yes. But doing nothing, staying here, losing our curiosity and our drive to explore - that's not only dangerous, it's suicidal. Maybe you think we don't deserve to survive. Maybe, because we've produced serial killers and pedophiles, and despoilers of the environment, and hedge fund managers, you would condemn the whole human race to purgatory. Well, see, by even pronouncing that opinion, you're proving the opposite: because you are not a rapist or a thief or a drug pusher, and you condemn those activities, you're showing that we do, in fact, deserve to survive. I have a dream that, one day, someone will stand on the Moon, look up, and witness the Sun slipping behind the limb of the Earth. That we'll have a thriving colony on Mars. That, eventually, some of us will leave our home forever, sailing out to explore the billions of stars in the galaxy, and perhaps even the billions of galaxies beyond. Will we find other life? Almost certainly. Will we find Vulcans or Klingons? Almost certainly not. Wouldn't it be better to know than to speculate? This is what we're for. Let's do it. Give us space. |
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