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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10 Most Recent Blog Comments:

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

October 2, 2021 at 12:02am

#1018506

I Will Get My Revenge

Today in New Stuff We Just Made Up For Attention

‘Revenge Bedtime Procrastination’ Is Real, According to Psychologists
You know that thing where you stubbornly stay up late for no reason because you feel like you didn't get any time to yourself? Here's how to stop.

Okay, so not "today," but way back in January. Whatever. "Revenge Bedtime Procrastination" is a goddamn stupid name for this phenomenon and nothing is going to change my mind about that.

It’s late and you’re exhausted. You barely had time to eat dinner and shower after work. Maybe you watched a few episodes of a show, read a chapter of your book, struggled through your skin-care routine. Now you’re in bed, and you know you should sleep.

People have time to watch a show AND read a book? And what's a skin-care routine?

But you keep scrolling—past the point that feels good. Your eyes start to close and you have to be up at 5 a.m. for work, but you’re not ready for rest. Some part of you is unsatisfied.

This activity has a name: bedtime revenge procrastination.

But it was called "revenge bedtime procrastination" in the headline. Either way, it's a goddamn stupid name.

It’s deeply validating to learn that this habit has a name, and that you are not alone in doing it.

Oh, wonderful, you've achieved validation. How nice.

“Where people will refuse to sleep because they don’t have much control over their daytime life, so they will sleep very late at night, even if they’re super tired, because they just don’t want that free time to end at night, and they don’t want tomorrow to start?”

I just figured this was Toddler Mode. You know, you're a kid and your mom says "Go to bed," and you cross your arms, stamp your foot and go "NO! Don' wanna!"

“There's lots of research showing that feeling like you have a bit of free time is super important for well-being,” she says. But at the same time, “many of the problems that drive revenge sleep procrastination—feeling depressed, being too burned out to enjoy your day, and so on—can be helped by simply getting more sleep,” she adds.

Oh. That's very helpful. The problem is you don't want to sleep and it can be alleviated by getting more sleep. Did someone take out student loans to be able to say that? Also, now it's a third formulation of the phrase. I get that it's a translation from Mandarin (says so near the top of the article.) Still, you'd thing English speakers would do their usual shoehorning of a phrase into an acronym.

You can also do more to optimize the time you do spend on your nighttime “revenge,” she says.

I think at least part of the problem is too much optimization. How about... stop optimizing everything?

“Often, when we get free time, we flop down and watch TV or scroll through social media. These leisure activities don't really give us the well-being bump we assume.”

Have you tried drinking or smoking weed?

So, okay, I will agree that this is a Real Thing -- I did it some when I was overloaded with work -- but I also maintain that the name of it is the stupidest fucking thing I've seen in a long time. So...

Merit Badge Mini-Contest!

Can you come up with a better name for this phenomenon? It can be serious or funny. It can turn word salad into an acronym if you want, or it doesn't have to; whatever you think it should be called. I have to admit I'm at a loss, myself, but I just can't keep that stupid name for it in my head. The one I like best will get its attractive and creative author a Merit Badge tomorrow. Deadline as always is midnight tonight, Saturday, October 2, WDC time. But if you can't think of one, feel free to comment anyway (even if you disagree that it's a stupid name).

8 Like • Comment • View 8 comments

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