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.

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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

March 24, 2023 at 9:31am

#1046915

Advisory

Let's do another random prompt from "JAFBG"

[XGC]...

Share some of the worst advice you've ever heard or received.

Thing about bad advice is that if it's really bad advice, then it's blindingly obvious that it's bad advice. Well, I should say "blindingly obvious to anyone with a rudimentary brain," because apparently, people have actually attempted to charge their iPhones in a microwave.

No, what's worse is advice that seems, at first glance, to make sense, until you actually do it and face the consequences. Something like... "You know, you should always carry a balance month-to-month on your credit cards, to build your credit rating." Yeah... no. Oh, it might help with the credit rating compared to not using credit cards at all, but you'll end up paying loads of interest. The correct solution is to use the credit cards and pay them off in full at every billing cycle; there's usually a grace period before interest kicks in. (This applies in the US; I don't know about other places.)

Another lousy one is "follow your passion." I've no doubt it works for some people, especially people whose passion is lucrative. But, like, if your passion is video games, maybe pick something else for a career. Everything I've heard about the video game industry makes it seem tantamount to slave labor, which is enough to make your passion not your passion anymore. Maybe take up knitting.

On the other hand, "passion" used to be a synonym of "suffering," so maybe that's not as bad a piece of advice as I'm making it out to be.

I also can't abide "Be creative." I'm no expert on creativity, especially in other people, but for me, it's not something I can do on demand. "Oh, I need a special word here. Something different and unexpected. Something creative." "..." (8 hours later it comes to me) "Goddammit."

Which is related to the common writing advice, "Write what you know." While not inherently bad, it's constraining. I prefer "Know what you write."

But, by far, the worst advice you can ever give or receive?

"Be yourself."

First of all, it's literally impossible to be, say, Robert Downey Jr., unless you're actually Robert Downey Jr. One has no choice but to be oneself. At least, with current technology.

Second, and perhaps less literally, you know when you're really yourself? It's when you're, like, taking a shit and picking your nose at the same time. Best not to do that in public, you know. Or maybe during sex, with your inhibition transmission stuck in neutral. No one wants to see you having sex in public, do they? Well, I guess some people do. I won't kink-shame. But the vast majority of us would prefer you keep that behind your curtains.

No, in most situations, you don't want to be yourself; you want to be the best version of yourself.

As for how to do that, well, I'm all out of ideas for the day.

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