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

February 17, 2023 at 12:01am

#1044972

Social Greases

Before I get into things today, please note that for the next few days, blog entries will be at unusual (for me) times. My birthday's coming up and I'll be drinking.

Today's article is another one that's (partially) about tipping. I didn't expect another one to come up so quickly, but such are the dangers of using random numbers.

Do You Know How to Behave? Are You Sure? How to text, tip, ghost, host, and generally exist in polite society today.

No, I don't know how to behave, beyond always returning my shopping cart to the corral or standing on the right side on an escalator. But it's always fun to see what so-called experts have to say on the subject.

Our social graces have atrophied.

Speak for yourself. If I had "graces," I wouldn't be the misanthropic hermit I am today.

We wanted to help. So we started with the problems — not the obvious stuff, like whether it’s okay to wear a backpack on the subway or talk loudly on speakerphone in a restaurant (you know the answers there).

I think I do. Yes, and yes. Going only by what I've seen in NYC.

By the way, who the hell decided it was fashionable to hold your dumbphone like a slice of goddamn pizza? For fuck's sake.

From there, we created rigid, but not entirely inflexible, rules.

That's a contradiction. Also, if the rules are so rigid, why do they change often enough that these articles have to come out every year?

There's a lot of these, so I'm just highlighting the lowlights.

1. You don’t have to read everyone’s book.

I take this one as a personal affront.

3. Don’t be loudly naïve about dating apps if you’re in a relationship.

I sometimes used dating sites (before there were apps) back in the time when most people thought they were dangerous. Now that everyone else is using them, I don't want anything to do with them.

4. When shopping with a friend, don’t cut them in the rack.

Someone needs to explain this to me. On second thought, no, don't. I never shop with friends.

6. Never wake up your significant other on purpose, ever.

Never wake them up accidentally, either.

10. Straight people can use the word partner only when they’re trying to get something out of it.

Bull. Shit.

12. On a date, all individuals present should gently and politely compete to pay the entire bill.

No. They want to pay? Let 'em pay. (This may be why I haven't been on a date in 23 years.)

Skipping a whole lot of other ones, mostly concerning dating, because I don't care.

26. If someone mispronounces a word but you knew what they meant, move along.

On the flip side, if someone misspells a word (or, worse, mistakes its for it's or vice versa, or things to that effect), set 'em straight.

28. Don’t ask people how they got COVID.

29. Or why they’re wearing a mask.

No, please ask me why I'm wearing a mask. Depending on my mood, I might answer with "to mess with facial recognition," "because I get compliments on my cat mask but never on my face," or "to keep you from running away screaming."

30. When casually asked how you are, say “Good!”

Valid only in English-speaking countries. And not even then; if someone asks me that, I assume they really want to know.

34. Actually, it’s great to talk about the weather.

It was 60 degrees in January. There’s lots to say.

No. Talking about the weather is just going to start an argument about climate change. It's now a topic more fraught than sex, politics, or religion.

38. Always wink.

What the bullshit is this?

47. Listening is not the time for you to silently rehearse what you want to say next.

Say something interesting, then.

51. No deciding your order at the counter. When you roll up, speak up.

NO SOUP FOR YOU!

78. Don’t talk about a movie when leaving the theater.

Oh, but one of the highlights of my life was shouting out "I can't believe Snape killed Dumbledore" while walking out after that one movie.

84-91. There are new rules of tipping.

This might irritate or confuse you, but the reality is there are new social expectations around what deserves a tip.

Finally got to that.

Also, as per my post a few days ago on tipping, bite my ass.

110. Saw someone shoplifting? No, you didn’t.

Ditto for jumping the turnstile.

Snitches get stitches.

120. Even when a kids’ party says “no gifts,” you’re supposed to bring a gift.

Bite my ass harder. Not limited to kids' parties (which I don't go to anyway), but how absolutely moronic is it to do the exact opposite of what a person says?

The list goes up to 140, though most of the explanations are mercifully short, and there are sidebars with even more inanities. If you make it through to the end, congratulations, and go ahead and do what you want anyway (within the boundaries of being mindful of other people).

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