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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Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

November 2, 2019 at 12:03am

#968797

Meeska and Jouska

PROMPT November 2nd

Write about jouska.

From Psychology Today, jouska is defined as “a hypothetical conversation that you play out over and over in your head. For example, replaying an argument in your head where you say all the right things and “win” the argument, or practicing asking your boss for a raise and playing out his or her responses and your comebacks.”

Jouska is why I'm single.

Doesn't everybody do this? It's basic self-programming. In the "replay" scenario you're practicing for similar situations in the future, and in the other scenario you're training yourself to deal with different responses.

The trick to being a jerkface asshole is when someone comes to you having practiced the conversation in jouska, you say something that they could not possibly have thought of in their practice. Example:

(Employee slinks in, hat in hand) "Um, boss, sir, may I have a raise?"

Boss: (pause for effect, then) "Tell me, Widders, what do you think of pomegranates?"

There's absolutely no reason you should allow yourself to play to their jouska script. If you do this, though, you have to practice jouska yourself just so you can come up with off-the-wall, non-sequitur responses to any rehearsed conversation. I mean, in the above scenario, presumably the peon has practiced this with the boss giving different levels of "yes" "no" "maybe" and "why" responses, and they've got all kinds of data backing up why they should get a raise, including having come to work on time even with measles, securing a multi-million-dollar contract for the company, and their kid has cancer. None of this matters; your job as boss is to make sure they don't get a raise. They're not expecting a conversation about pre-Raphaelite paint mixing techniques, so give 'em one.

On the peon's side, even though you know this could happen, you practice jouska anyway, right? Like I said, everyone does it. Sometimes you lie awake at night, staring into your old friend the dark abyss, replaying a conversation until you've convinced you monkey brain that it went your way, after all. Or you're worried about the meeting tomorrow so you play out different scenarios, remembering to be ready for loops thrown at you involving pomegranates or paint.

But not me.

No, I don't run variations on the script until things go my way, because I know things won't go my way. I run scenarios until they involve the worst possible outcome for me. There's a good reason for that: I only like to be pleasantly surprised. It's the same reason I'm pessimistic about everything. If I go into a situation expecting, or even hoping for, a good outcome, I can be disappointed. If, on the other hand, I go into, say, the doctor's office expecting a cancer diagnosis, then if it is not cancer I can feel the pleasure of relief; whereas, if it is cancer, I can feel the euphoria of having been right.

Which brings me to why I'm single. Every time I think about meeting someone, the jouska goes something like this:

Me: "Hi, my name is-"

Her: *PEPPER SPRAY*

Or this:

Me: "Let me buy you a drink."

Her: "I was just leaving. With my husband. The pro boxer."

Or this:

Me: "Hey, let's talk about pre-Raphaelite paint mixing techniques."

Her: "Zzzzzzzzzz..."

I think some guys, they go into potential relationships, and they like to skip ahead in their minds to the part where they're both naked. Maybe some chicks to that, too; I don't know. Point is, some people just kind of wing the whole "get to know you" part and rush to the "let's get the lube" part. In other words, their jouska involves playing out the clothes-on scenes in such a way as to get to the R-rated movie as quickly as possible.

But not me. No, whenever I meet someone I think I might be interested in dating, my mind doesn't skip ahead to the date, or to the sex, or to the breakfast afterward, or to the trip to the Paint History Museum. It skips right to the part where she's had enough of my bullshit and storms out the door for the last time.

Knowing she'll leave me for some Australian dingo-fucker is enough to keep me single.

Now, look, I know this might come across as me having a low opinion of women. Think about it, though - if I had a low opinion of women, I could probably convince myself that I could attract one and keep a relationship going. It's myself that I'm certain is unworthy, not anyone else. Proof? Well, what's the one thing women say they look for in a partner? Looks? No. Money? No. Muscles? Gimme a break. Six-pack abs? N-well, maybe. Probably it helps. Cats? Definitely not. No, it's a sense of humor. You may not like my sense of humor, but I think we can all agree that I have one, yes? Yes? Okay. Good. And yet I'm still single. Q.E.D. I have the one trait that heterosexual women claim to be looking for in a male partner, and still can't stop being single.

Consequently, it's me. Therefore, my jouska will continue to justify this to myself.

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