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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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March 1, 2022 at 8:57am
March 1, 2022 at 8:57am
#1027699
Still in California for the next couple of days.

No more observatories to visit yesterday, but at least there were breweries.

One well-known feature of the L.A. area is landslides. We took a drive around a place that's known for its landslides, marveling at all the doomed houses all built to appreciate a view of the ocean. I'm thinking a lot of them will get a much closer view of the ocean at some point. Oh, and did I mention there's also a fault line involved? Fun!

I've got a pretty tight schedule today so this entry's not going to be as substantial as usual, but as I wanted to get something in, here's a bit about where I'm hoping I can manage to get to today.

https://en.wikipedia.org/wiki/Santa_Catalina_Island_(California)


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