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Rated: 18+ · Book · Personal · #1196512
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.




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October 10, 2024 at 12:09am
October 10, 2024 at 12:09am
#1078033
And so it ends, as I'm returning to the US today.

As appropriate, I spent some of yesterday drinking, mostly beers that I've wanted to try but hadn't had the opportunity.

I did participate in my final tour of the trip, another session of walking around Brussels, but this time with an emphasis on its food. And, in case I haven't mentioned this before, Belgium has awesome food.

Going to keep this short so I can finish final packing. Since I've had very few problems on this trip, I can expect the flights back to be horribly delayed... at least. Look, it helps to expect the worst, right? Well, delays aren't the "worst," but if the worst happened, I wouldn't be around afterward to crow about being right, now, would I?

I'll just leave you with the dog version of the Manneken Pis from yesterday:


 
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