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 20, 2020 at 12:01am

#1000530

Carol of the Hells

"30-Day Blogging Challenge ON HIATUS" [13+]:
20. Go Caroling Day
Have you ever gone caroling, or had a group of carolers show up at your door?
Write something about caroling.

"JAFBG" [XGC]:
This is the most wonderful time of the year! Now, tell us why that's total bullshit.

Now there's an appropriate combination of prompts if there ever was one.

Look: it's not my intention to shit on someone else's festivities. I get depressed around this time of year, same as lots of people, and I'm not going to begrudge anyone the ability to do anything to try to pull themselves out of a funk, or celebrate whatever.

But listen: holiday music makes me all stabby. I know I've talked about this in previous entries. It doesn't fix my depression; the best it does is turn it outward, to anger. While I've never lashed out at anyone physically, and expect I never will, I do get vocally angry, my temper on edge, and I don't want to be around people when that happens because, like I said, I don't want to shit on anyone's day.

The kind of music that does cure my depression is depressing music. That kind of music makes me happy. But you don't see me blasting it in elevators and stores and waiting rooms and entire radio stations, convinced that all anyone has to do is listen to Leonard Cohen to make themselves feel better, because I know that while it works for me, it's not going to work for everyone.

If I'm not in a bad mood, and carolers are about, I can mostly ignore them. If I am in a bad mood, they just contribute to worsening it.

And that's one reason why this is not the most wonderful time of the year: it assumes that all anyone needs to feel joy is some blinky lights, catchy music, and consumer spending. Such things seem to work for most people. But it's like if I assumed that, for instance, thick incense smoke is all that anyone needs to cure what ails them and so I'd go around in a haze of sandalwood and patchouli. I'm sure some people would appreciate that, but I'd wager that others would consider it annoying. Well, all the bright sparkly glittery cheery shit everywhere is like that for me.

Worse, people have been programmed by years of "holiday stories" all the way back to Dickens that anyone who's not on the ho-ho-ho bandwagon is automatically a Bad Person by definition and needs to be dragged by a blinking string of lights attached to a cadre of reindeer into a forest of decorated fir trees. And I don't know; maybe I am a terrible person, but mostly I just want to be left alone until the cheer firehose gets turned off and we're back to the normal cold dreariness of winter (although don't get me stared on valentine's day either). I don't need to see sparkly lights or hear jingly bells, I don't need to be caroled at, and I certainly don't need to be subjected to peoples' inevitable family drama.

But for the sake of the people who do enjoy such things, I'm usually less vocal about it in life than I am in here.

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