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.

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

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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

September 11, 2022 at 12:01am

#1037608

Accountability

Today's article (actually an essay) has been languishing in my queue for a while, and today is its day. I don't have a lot to say about it, and it may be of only marginal interest to most people, but I found it to be an interesting glimpse into some of the cultural tensions that we've been experiencing.

The Ticking Crocodile: Performative Accountability in Cultural Institutions
How to spot false gestures at accountability, why acknowledgment is not enough, and what genuine reconciliation might look like

And it's a good thing I don't have a lot to say about it, because I'm really not in the mood today. Yesterday would have been my dad's birthday had he survived (he was born 105 years ago), and I've been practicing avoidance. It's raining, the days are getting shorter, and things are getting colder. I know a lot of people love fall. I do not. I'm a summer guy. If it's too hot for you, it's just right for me. Anything below 20C is "cold" and anything below 15C is "freezing" as far as I'm concerned, and the rain just makes me more miserable. The only good thing about the approaching season of dying is beer: Oktoberfest lagers and pumpkin ales make their brief seasonal appearance, and I might have had a few of those yesterday.

None of which has anything to do with the article (except for maybe the "avoidance" bit), but dammit, this is my blog and I get to rant about my state of mind if I want.

So I'm just leaving the essay here for your benefit. I'm taking a mental health night. I did read it (twice - once when Turkey DrumStik

sent it to me and again just now to see if I had any coherent thoughts about it, to which the answer is "not really") but while I think it's important, I'm in no mood to articulate exactly why. But it does have implications for my life, and for that of my father before me (I knew he'd figure into this somehow). I spent my childhood on land appropriated from an Indigenous people; I've donated the artifacts found on it to their tribal council, but is that the end of my responsibility, or just the beginning? Or is it even on me at all?

I don't know, and in a few years, it won't matter anyway.

7 Like • Comment • View 1 comment

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