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.

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

March 15, 2023 at 9:29am

#1046411

Stupid Answer

Now, one from "JAFBG"

[XGC]:

What's the stupidest question you've ever been asked?

As tempted as I am to glibly answer, "This one," that would be both unfair and untrue. The problem is, out of all the stupid questions I've been asked, it would be very difficult to pick just one. Plus, my mind blanks on most of them. I selectively edit them out just like I edit out the stupid questions I've asked, except at 3 am when I lie awake going "Why did I ask that lady with the chihuahua if her dog was a Dachshund?" (Or whatever.) Everyone's mind blanks at some point, even mine.

I've never worked retail, though, so I suspect I've been spared the worst of the depths of derp. Things like pulling an item off of a display with a great big ALL ITEMS $4.99 sign above it, with $4.99 stamped on each instance of the item, and then turning to the nearest employee and going "Excuse me, how much is this?"

It's a good thing I don't work retail, because in such an instance, I'd be sorely tempted to go, "That? Oh, that's fifteen bucks, cash only, and I can help you with that."

Anyone smart enough to ask a question has enough intelligence to realize that they don't know everything, so I tend to be somewhat forgiving (believe it or not) of ordinary stupid questions. There are exceptions, though, like when someone asked me "Why isn't there a White History Month?" (If you need to know why that question is stupid, go Google it before asking me.)

Some questions seem stupid, but they're really attempts to strike up conversation. At the moment, though, I don't always recognize that, but then, like four weeks later, I'd be like, "Oh, they were just trying to find something to talk about."

Which leads me to what might well be the stupidest question I've ever been asked, which, in the grand scheme of things, really isn't all that stupid, but, like I said, I tend to blank these things out.

Scene: I'm in a senior facility visiting a friend's elderly grandmother who, while physically less than able, still had her mind, hearing, and vision. We'd stopped at a convenience store to get some things for her and also for us. One of the things I got for me was a bottle of Coke. Like, the trademark wasp-waisted bottle with the red label and distinctive cursive Coca-Cola logo in white. Absolutely unmistakable for anything else. I pull this thing out and take a slug.

And Friend's Grandma asks me, "Do you drink Coke?"

Before you pass it off as a "senior moment," like I said, this lady was sharp as nails, usually. If I'd been less stupid myself, I'd have answered something like "No, I just use it to clean battery terminals." But no, I was taken off guard by being asked if I drink Coke as I was sucking on a bottle of actual Coke. So I think I just nodded.

Again, though, it occurred to me like a week later that she was just trying to find an entry point to a conversation.

Such a thing, however, is the nature of some stupid questions, and if you can't tell the difference, there in the moment, between actual stupid questions and awkward overtures, well, then, who's really the stupid one?

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