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

October 3, 2022 at 12:03am

#1038519

Blender

Entry #2 for "Journalistic Intentions"

[18+] today.

Justin Sutherland

Having never heard of Justin Sutherland, I was relieved to discover he's not the illegitimate love child of Justin Bieber and Kiefer Sutherland. My relief was short-lived, however, as it became clear that the above linked "article" is a barely-disguised ad. Fortunately, it's mostly an ad for a book, which I've repeatedly stated isn't going to stop me from linking it on a writing site.

Anyway, it turns out that Sutherland is a chef, though someone I'd never heard of. Not that surprising, as I don't follow celebrity chefs and I don't live in Minnesota.

Sutherland was boating with friends on the St. Croix River on July 3 when his hat blew off, causing him to reach for it. At the same moment, the boat hit a wave, sending him into the water near the propeller, which "did a number on his head and left arm,"

Sounds like he was more than "near" the propeller. I guess you could say he got screwed.

Look, I'll never pass up an opportunity for a pun, no matter how tragic the incident that prompts one. I'm not making fun of the accident; it sounds like no fun at all, one of those shitty things that occasionally happens to people.

Here's a snippet of Sutherland's interview. You can watch his full appearance on The Jason Show in the player above.

No.

Jason: What do you remember about that day?

Sutherland: I mean, honestly, I remember everything. It was a beautiful, perfect, you know, day. I remember everything from hitting the water, to getting slammed back to the boat, and to getting to the ambulance.

The key word being "was." One wonders how much booze was involved, though a large amount wouldn't work with remembering "everything."

Jason: I know this seems very simple, but you don't remember any of the pain?

Sutherland: No. Not a single piece.

I ain't no doctor, but that sounds like shock to me.

Jason: You look fantastic!

Sutherland: Regions

Apparently this is a hospital in St. Paul
was amazing … I still haven't eaten solid food in nine weeks now. I have five metal plates in my face. And this is all brand new (pointing to his face), I can't put any pressure on my teeth. I've lost about 14 pounds, trying to drink protein shakes.

That sucks and all, but at least he's a chef: those protein shakes were probably amazing. For protein shakes.

Jason: Let's talk about the positive … the positive is the support. Wow. … What did that feel like?

Sutherland: Incredible. … Nothing but just gratitude. We touch a lot of people in our lives … but sometimes you don't realize the people you cross paths with and the lives that you impacted. The people that came together – still, eternally grateful.

You know, this is kind of refreshing. So much so that I'm willing to overlook the whole "positivity" thing. Why? Because he wasn't all "God healed me." No, he acknowledges the very human, very skilled people involved in his recovery. I don't see a lot of that in the news. I see a lot of "That tornado ripped through and slammed me against a trailer and I couldn't walk for a week, but God healed me," ignoring the neurosurgeon that fixed the walking thing. Or, "I was driving drunk and slammed into a tree, but after a month I could see again, thanks to God," without mentioning the doctors who fixed your unworthy drunk-driving-ass face.

Never mind that God did those things to you in the first place. I mean, if he's in control, then didn't he both send the tornado *and* heal you afterward? If not, then he's not all-powerful, is he? And if he does, why only praise him? It's like, occasionally you'll get a firefighter who lights shit on fire and then swoops in to play the hero. We call them "arsonists" and they generally get arrested for it.

Or maybe the initial incident was some combination of your fault and the random workings of the universe; the medical attention you get afterward, though, that's deliberate. No need to resort to supernatural causes.

Don't get me wrong; I'm not condemning people who have faith that they think helps them get through a tough situation. Whatever brings you comfort. But all the work done to fix your broken ass? That was people. Humans. Sure, some of us suck, but we can also be quite clever, competent, and helpful. Well, not me. But doctors and EMTs and such. Not to mention any of your friends and family who help you through it all.

Point being, it sounds like this guy acknowledges that.

Well, the rest of the article is the ad for his book and his restaurants, and you can look at that part if you want. As for me, next time I'm in the area, maybe I'll remember this and check out one of those restaurants. After all, that's one of the reasons I travel in the first place.

I just hope they're serving solid food.

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