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.

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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

January 28, 2021 at 12:16am

#1003039

Nope

PROMPT January 28th

We need your help filling the Challenge War Chest! In your entry today, write three of your own prompts and then use one of them to complete the rest of your entry.

1. What is something you're afraid of? You don't have to reveal your biggest fear, just pick something that gives you the willies, rational or not.

2. Talk about a time when you wish you'd handled something differently.

3. What sounds do you dislike?

Now, I could probably come up with something for all of these, but I'm not known for being an overachiever. Besides, if I participate in future rounds, I'll want to save some of my answers for them.

So I'm going to talk about #1.

As noted in the prompt, it's not my biggest fear, but I'm not a fan of anything touching my eyeballs. I could never wear contact lenses, because that would involve me touching my eyes, and that's not going to happen. Oh, sure, I'd probably get used to it, but the point is I don't wanna. Nor have I ever had to; until recently, I've had pretty good vision.

This is in spite of eye surgery I had back in the 80s. I'd injured my cornea doing construction work. You know how they say "always wear safety glasses?" There's a reason for that, and it's not fashion sense. In my defense, I had been wearing some but they weren't the OSHA approved kind, so they slipped off and fell down a stack of cinderblock cells, frustratingly out of reach. They're probably still the wall of a garage in Reston. But I had to keep working, so there was nothing protecting my eyes when a nail flew up and smacked my cornea.

The next day, I got stitches in my cornea. This sucked, but at least I was under general anesthesia for the actual surgery. Within a year, though, it had completely healed, and my vision in that eye had actually improved some.

About fifteen years ago, though, I started feeling eyestrain. Apparently it's just one of the fun parts of getting old that you can't focus at different distances anymore, especially if you spend your days in front of a computer, which describes my life. So I started needing reading glasses. Still no contacts necessary, and hell, glasses are cool.

But even more recently, it's become apparent that my vision is deteriorating again, and I will need eye surgery. Again.

I looked up the procedure and went, "Nope."

Apparently this surgery is really common, and they have sorcery now, so it's actually an outpatient procedure -- the patient is awake for the whole thing. The idea of letting someone fuck around with my eyeballs, no matter how good they are at their job, while I'm awake and aware, just freaks me right the hell out.

One of the most horrible things I ever heard of was some guy who was having eye surgery. The anesthesia only partially worked: he could not move, he could not speak, he could do absolutely nothing -- but he could see and hear. So everything the doctors and nurses said and did? He was awake for that. With his eyes wedged open because, in case I wasn't clear, this was eye surgery.

I can't think of too many things that would freak me out more. Bad enough I have sleep paralysis sometimes.

I mean, lots of people are blind, right? I could be blind and not have to deal with this.

But. Hell. That would make video games difficult, and driving problematic. (On the other hand, tax break!)

So I'll probably suck it up and get the surgery. At some point. Because this shit isn't going to get better on its own.

Getting old sucks, but I suspect it beats the only alternative.

9 Like • Comment • View 10 comments

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