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

November 27, 2021 at 12:02am

#1022387

Go Home

Well, this one has all the potential for disaster.

PROMPT November 27^th

Things have progressed well in your town/city with the Pandemic. So well that you've been allowed to return to the office instead of working from home. Your co-worker Karly, is sneezing and coughing and refuses to wear a mask. Who do you call, or do you let it slide. Tell us why you would act that way.

I'm going to weasel out of this with "insufficient data."

Well, not really.

This is already a highly hypothetical situation, as I haven't worked in an office in over ten years (I worked from a home office for a while before I retired).

Enhancing the hypotheticalness of it is the idea that I would be "allowed" to return to the office. No, given a choice, I'd keep working from home. If we're talking about my actual career here, and not something fictional (to continue the hypotheticality), there's no reason for me to be in an office 95% of the time. I know some people who would rather work in an office than from home, and that's fine too, but we're talking about Me here.

Karly's an asshole. But my response depends on a lot of factors unclear from the prompt. Am I still in charge? Probably not, if I'm not the one making the decision about working from home or in an office. Because if I were in charge, I'd fire her ass on the spot. (I live in a state where I can do that).

Since I'm not in charge, though, there is a lot of missing information here.

1) Who else is in the office? If it's just me, I wouldn't be overly concerned about it. Assuming it's the 'rona and also assuming other things conforming to reality, being vaccinated means my chance of severe problems is probably less than the chance of me getting into an accident on the commute. Therefore, it's other people I'd be concerned about. And clients.

2) What is the company policy for shit like this? I'd want to follow that. If that means being a snitch, I'll be a snitch.

3) Is KarenKarly above, below, or equal to me in the corporate structure? It matters.

Most likely, I'd just want to go back to working from home. It's my preference anyway.

People are fucking crazy with this stuff these days, and they've turned it into a political issue, which I prefer to stay away from (most of the time). I've bitched about it before in here, and I see no need to repeat it, or go off on a tangent about it.

I will say this, though: I definitely think less of people who are inconsiderate of others. I say that as someone who generally doesn't give a shit about too many other people, but I still don't do stuff that actively endangers them. It's like how I live an alcohol-positive lifestyle, but I'm very, very careful not to drive drunk. Drinking only affects me. Driving drunk can cock up someone else's day.

I treat the unmasked and unvaccinated like a smoker in a restaurant. That shit used to be acceptable; it no longer is, because of studies about the effects of second-hand smoke. Same thing. Actually, I'd rather be around second-hand smoke; it's safer. Though I do understand there are legitimate reasons to not get vaccinated; "I don't wanna" isn't one, and neither is "it's against my religion."

And that's all I'm going to say about it. Today.

9 Like • Comment • View 8 comments

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