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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Adherennium Plotting something

about 2 hours ago
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Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

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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).

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Nov 7, 2024 at 10:58am
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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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May 12, 2024 at 9:33am

#1070954

Revisited: "Under Pressure"

In nearly 1700 entries over almost two decades, the only shocking thing is that I haven't repeated titles more than I actually have. Going back in time today, I'm going to resurrect the entry with this title from June of 2020: "Under Pressure"

The linked article itself, from six months earlier, is still around.

Not too surprising, since it's from Atlas Obscura.

In the entry, I started with:

Turns out that, like gravity, crumpets, Doctor Who, and Russian Imperial Stout (no, really), champagne was a British innovation -- and the reason why will shock you! (Hey, look, I can write clickbait! Pay me!)

Do they still use that kind of clickbait title? I don't think I've seen it in a while. I'm guessing people get wise to the tactics so they no longer work, so they move on to different, more subtle tactics.

Anyway, none of this is clickbait.

Also, it is now canon that the Doctor went back in time, met Newton, and changed history by leading him to create the Theory of Mavity, not gravity. Well, it was actually his companion's fault, but that's not the point.

I also wrote:

They only lost 10% of their forests and timber supply? That doesn't sound so bad. Oh. No, the author is just misusing "decimate."

While I will never not be pedantic about the definition of "decimate," I get that it's a futile battle.

Since there's really not much else I found to criticize about that four-year-old post, I'll just point out that I did, eventually, tell the story of Russian Imperial Stout... two years later, in this entry: "The Yeast You Can Do"

So, bonus link there. Fear not, though; it's short. Like today's.

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