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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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

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JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

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Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

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Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

March 22, 2021 at 12:02am

#1006850

Mad Scientist

There's a reason that the "mad scientist" archetype exists.

Nikola Tesla: The extraordinary life of a modern Prometheus

This article is from last August, and it speaks of a biographical movie about Tesla -- one which, apart from this article, I've heard nothing about. But long ago, I read a few books about him, and so I sometimes forget that many people only know the name because of Elon Musk or, sometimes, a mediocre band.

The opening of a new biopic of Tesla provides a timely opportunity to review the life of a man who came from nowhere yet became world famous; claimed to be devoted solely to discovery but relished the role of a showman; attracted the attention of many women but never married; and generated ideas that transformed daily life and created multiple fortunes but died nearly penniless.

That's a decent enough summary, I suppose. Read the article for details; I'm not going to paste a lot of it here. As a bonus, there are some awesome pictures.

Essentially, without Tesla, life today might have been very, very different. Oh, sure, most of his inventions would have been created by someone else eventually; such is the nature of inventions. But every once in a while, a whole lot of genius is concentrated in a single person. Everyone is familiar with Einstein and Newton; Tesla's main rival, Edison, mostly just had a big team and competent public relations. (Ironically, Elon Musk himself is more of an Edison than a Tesla)

Also, as you'll see, Tesla was the very definition of "eccentric," which I'm sure didn't help much in the publicity department.

His money long gone, Tesla spent his later years moving from place to place, leaving behind unpaid bills. Eventually, he settled in at a New York hotel, where his rent was paid by Westinghouse.

Amusing thing about that hotel: it's still around. Well, it's a hotel again, anyway; for a while there it was some cult headquarters or something, but now it's once again the New Yorker hotel, and it's located not far from Penn Station, in midtown Manhattan.

I stayed there once on a trip to New York, and while I didn't get Tesla's room (I didn't want to be That Guy), I made a pilgrimage to the floor it was on and stood outside the door.

Sadly, I didn't feel a spark.

Fortunately, these days, thanks to a few movies and such (one of which, The Prestige, had him portrayed by none other than David Bowie), more people know about Nikola Tesla, but I'm leaving this here just in case. The article is short, and really just hits the highlights.

Maybe I'll see if I can track down the biopic mentioned in the article.

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