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').

1 Like

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

1 Like

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

December 24, 2020 at 12:01am

#1000762

Land of Nog

"30-Day Blogging Challenge ON HIATUS" [13+]:
24. Last-Minute Shopper's Day also National Eggnog Day
I should think good strong eggnog would hit the spot after a day of shopping.
See what you can come up with for that one.

Now, look, we all know that I put the "pro" in "procrastination." Hell, the only way I can manage to usually post one of these entries shortly after midnight is to pretend that I'm doing yesterday's entry and submitting it late.

But when it comes to holiday shopping... well, I was done with that weeks ago.

Part of this is because I, by design, have only a few people to shop for. But another part is that even in the Before Time, I didn't go into stores unless I absolutely had to. And by "had to," I mean going into a liquor store because my state has backwards-ass rules about not being able to mail-order liquor.

Everything else, I can and do buy online, issues with Amazon be damned.

Yes, even groceries. I know I've mentioned this before, but I've been having them delivered for at least two years, now.

Of course, there are a few local businesses I feel I should support, and I'll venture into those shops on occasion, but for the most part, everything I need for myself or as gifts for others comes from the internet.

Besides, if I went into stores on December 24th, I'd be subjected to holiday music, and that's a thing I would rather avoid.

Consequently, I don't have eggnog. It's just not something I think about. If I'd gone into the supermarket, I'm sure I'd have seen a display of the mix for it and probably bought it (another reason I don't go shopping: I have poor impulse control and shopping online tends to keep that in check). Then I could have walked across the parking lot and picked up rum at the liquor store -- although at the moment I don't have to because I have plenty of rum.

Now with this prompt I find myself wanting some eggnog... but not enough to make a special trip to the store later today, and finding a delivery slot on Christmas Eve just isn't going to happen. I've got supplies to last me at least through Sunday.

And don't start with the "why don't you make your own eggnog from scratch" shaming. First of all, it's a lot like work; second, and perhaps more importantly, I'd still have to purchase some of the ingredients, at which point I might as well get the pre-made stuff. So no eggnog for me this year. Maybe next year, if I think about it. But probably not.

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