Complex Numbers (Book)

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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.

http://www.ddewey.net/mandelbrot/

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February 14, 2022 at 12:02am

#1026662

Literately

As a reminder, I'm traveling most of this week, so updates may be at irregular times.

Since I still have to pack, this one will be blessedly short.

Poe Boy
The ongoing impact of Edgar Allan Poe

Article is from last October, which is when people actually remember that Poe existed, but anything about him is always timely as far as I'm concerned.

In the early hours of January 19, a shadowy figure glides into the Westminster Hall and Burying Ground through a side-gate and makes his way to a cenotaph. In the biting Baltimore night, the black-clad stranger — in wide-brimmed hat and a long scarf obscuring his face — stands staring at the raven engraved upon the cenotaph. He pours himself a glass of cognac and raises a toast. He bends down, places three roses and the unfinished bottle by the monument, and wafts softly away into the fog.

And already I'm getting a headache. The Poe Toaster (or, if you will, Poester -- okay, you won't, and neither will I) is a wonderful story, but I thought we were going to talk about actual Poe.

To be fair, the rest of the article does get to the point, or points, if circuitously and with precious prose unbecoming of a tribute to Edgar's own style. Poe famously traipsed all up and down the East Coast, and lots of cities claim him: Boston, where he was born; Baltimore, where he died; Richmond, where the oldest extant building in the city is now a Poe museum; Philadelphia, for reasons expressed in the article. And less than two miles from my house is the dorm room where he briefly lived while attending the University of Virginia, so we get a claim on him as well.

But he really belongs to everyone, and to no one.

Anyway, I won't quote more from the article, partly because it's all hooked together in typical epi-pseudo-post-après-modernist (or whatever they're calling the style these days) fashion (I can't resist the temptation to coin Poe-modernist), and partly because despite my personal grievances with the writing style, it's still worth reading.

And though I brought this article up at random, I find it darkly appropriate that it happened to arrive on Valentine's Day.

For the moon never beams, without bringing me dreams
Of the beautiful Annabel Lee;
And the stars never rise, but I feel the bright eyes
Of the beautiful Annabel Lee;
And so, all the night-tide, I lie down by the side
Of my darling—my darling—my life and my bride,
In her sepulchre there by the sea,
In her tomb by the sounding sea.

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