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.

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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).

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

August 20, 2023 at 10:34am

#1054349

Revisited: "Untruth and Consequences"

It's Sunday again, so we go back in time to a random entry from the past. This one's from March of 2021: "Untruth and Consequences"

This was very close to the 1-year anniversary of the pandemic being officially declared, with all the disruption that it led to. The entry itself, though, is a riff off a Cracked article about disinformation.

The link is, unsurprisingly, still there; disinformation is still rampant. Much of the entry, and the article, is as relevant as ever, if you discount the references to pandemic restrictions.

So I just want to point out a few things that slipped through the cracks (pun intended) last time.

Online Groups Are Getting Really Weird

What I might not have been clear about is that in the 30 or so years that I've been online in one form or another, there has never been a time when online groups weren't sometimes weird. Though things may have been easier to deal with in the days before everything was commodified, advertised, bowdlerized, centralized, and sanitized.

Yoga And New Agey Types Are Getting Into It

Humans usually find it easier to forgive or excuse the misdeeds of their in-group while magnifying those of their out-group. It's the difference between, say, "Boys will be boys" and "Lock up that miscreant for life." Or, "A [person in minority] stole my car stereo once, so I hate all [people in minority]" and "Almost all mass murderers and serial killers are white guys, but that doesn't mean white guys are mass murderers and serial killers."

It's important to guard against this tendency, I think. It's not a matter of "both sides are bad," but of recognizing that every demographic group has both good people and assholes in it. Except Nazis, of course. They are, by definition, bad.

The point is, if you're on the political left, for example, you might be tempted to think that accepting misinformation is tied to consuming right-wing media all the time, when the left (and make no mistake, New Age is definitely "left") is just as susceptible to faulty group-think.

The reverse is also the case.

I noted this in the original entry, but the above expands on the idea:

You won't hear me say "both sides are bad," but what I am saying is that bullshit doesn't take political sides; it's an equal-opportunity brain rotter.

I'll end this Revisited entry with what I still feel is the most important point, from my own perspective:

Once you start believing one unsupportable thing, you can be open to believing more. That's one reason I hammer on about science.

But hey, at least, this week, I didn't land on one of my infamous early short-ass blog entries. (In my defense, I think those happened before the Newsfeed existed.)

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