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Not for the faint of art. |
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. |
Congratulations! ![]() ![]() ![]() How do you celebrate your successes? Same way I celebrate my failures. That's one of the many, many beautiful things about alcohol. Had a major success? Drink! Suffered a terrible failure? Drink! Day was just okay? Drink. Of course, I'm aware that I'm privileged in that regard - not only to have access to some of the best fermented and distilled beverages created in the history of humankind, but also because I'm fortunate to not be an alcoholic. Thus, I can enjoy drinking, but I don't need it. I know some people will assert that this makes me an alcoholic in denial. Those are not people I want to associate with. Unfortunately, I won't be celebrating my successful completion of 30DBC in that manner; I'm still focused on weight loss and probably will be for several more months. But never fear - I'll make up for it when I go to Vegas. Like I said before, I haven't given it up; just cut back for the sake of calories. Same as with food. Here's a little secret to happiness, though: whatever it is you do to celebrate - sometimes, on occasion, do it even if you have nothing to celebrate. Because you really, really do, even if you don't realize it. Acknowledging that can only help you. And with that, I'm done for the month. Stick around, though - I've got a lot more to say. |