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Complex Numbers
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.




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January 6, 2019 at 12:47am
January 6, 2019 at 12:47am
#948990
What was the biggest news in your life from last year?

I didn't die.

Yep, that's about where I set the bar, these days.

Oh, sure, I did stuff: traveling, gambling, drinking. Went to Nerd Camp, which was one of last year's highlights. I got to drive a Tesla, briefly, in December. Started blogging again, for some reason. My housemate got a new kitten. But nothing's fundamentally changed, for the better or for the worse.

You know what? I like it that way. I've already achieved most of my goals in life, and what few remain, such as getting published, I'm ready to write off as a lost cause. Although I still have a few things I want to do, none of them ought to be life-changing, either. Things like doing a Scotch tour of Scotland and a beer tour of Belgium. Maybe spend a week in the Loire Valley of France drinking a variety of Vouvray. Hm, I sense a theme, here. Technically, I could do any of those things at any time, but while I don't mind traveling alone, I don't really want to travel by myself to a foreign country where I don't know anybody (I traveled alone to England once, but stayed with friends).

Want to know the trick to achieving all your goals in life? Aim low.

I know the common wisdom is the exact opposite of that, but look: the common wisdom is generally crap designed to sell advertising space. It's meant to keep you unfulfilled, like there's always something better just around the corner. They're not really trying to help you; they're trying to help Apple and Wells Fargo.

Because of that sort of thing, people seem to believe that happiness is about having what you want. It's not. It's about wanting what you have.

So anyway, the point is, I didn't achieve any milestones last year besides Not Dying. I consider that a big win. But I had some great experiences, hung out with cool people, and generally enjoyed life.

Nothing's changed, but that's the way I want it.


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