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🎶

about 22 hours 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.

2 Like

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.

1 Like

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.

1 Like

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.

3 Like

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

July 28, 2024 at 9:39am

#1074494

Revisited: "The Truth is Out There"

In another astounding coincidence, the random entry I picked to revisit today, from April of 2020, touches on many of the same topics I discussed last week: the search for alien life, and science in general: "The Truth is Out There"

Hell, it even has a similar title to last Wednesday's entry. Look, I'm closing in on 2800 entries here; I'll get there before August is out. I know some titles have been repeated. Sometimes, I make an effort to avoid reusing a title, but much of the time, I can't be arsed. This isn't even a case of reuse, but variation on a theme.

In any case, I consider last Wednesday's entry to be the update on my opinion on the subject of the search for extraterrestrial life, so I'll try to focus on other things I wrote back then.

I've been following this guy, PZ Myers, for a while now, and while I don't always agree, I appreciate his point of view. Except about movies.

I think I've linked his blog at least once again since then. Still reading his stuff, though he's become utterly obsessed with spiders. I don't hate or fear spiders, but I lack that level of obsession. That's not the only thing he posts. And I've grown to appreciate his point of view about movies, to the extent that he's a negative barometer for me: generally, if he hates a movie, I'll like it, and vice-versa. Especially when it comes to comic book adaptations. Just recently, he ragged on the Deadpool/Wolverine movie, which served to make me want to watch it more. Which I haven't, yet.

Thanks, Myers, you made me look up a word for the first time in years.

The word then was "apophenia." Since then, I've discovered even more words I had to look up (not counting those I chose to look up due to my interest in etymology, which is not the same thing as an interest in entomology, which doesn't include spiders). I count any day when I learn something new as a good day. Well, unless something bad happens to balance it out.

Pretty much everything else is either not noteworthy, or was covered in here last week. Except for a big fucking oops on my part, where I apparently pasted a quotation twice. I try to do some basic proofreading before I post these things, but sometimes, something slips through the process. Still not as bad as when I find a years-old typo. Those are truly embarrassing.

But hey, at least that's evidence that I don't post using Artificial Intelligence; anything I put here is either a quote or Natural Stupidity.

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