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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 8 hours 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

about 10 hours 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.

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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.

January 1, 2024 at 8:57am

#1061666

Gratuitous

Same shit, different year. Let's see what the random numbers have in store for this first day of '24 (hey, that rhymed)...

Uh oh, I gotta handle a New Yorker article while hungover? Curse you, random numbers!

Has Gratuity Culture Reached a Tipping Point?
Paying extra for service has inspired rebellions, swivelling iPads, and irritation from Trotsky. Post-pandemic, the practice has entered a new stage.

I've chiseled tipping articles in here before... including one almost a year ago which used the pun in their headline before TNY even thought of it: "Tipping Point"

Consequently, I'll try to limit my ranting to stuff I haven't covered before. I doubt I'll be entirely successful.

Before screens, tipping, like a marriage proposal, was a private affair.

No. People proposed in public prior to posting on Pinterest (or whatever).

Tips can reveal hidden values or the rumblings of the subconscious.

Mostly, though, they reveal who's an asshole and who's not, and a range in between.

A waitress’s breast size, for instance, correlates positively with tip size.

Correlation isn't causation. Maybe waitresses with ample bazooms provide better service. I should do a scientific study.

Etiquette experts studied the so-called guilt-tip boom.

And reached, mostly, the wrong conclusions.

Apparently, we now tip assistant sports coaches (up three hundred and sixty-seven per cent) and theatre-box-office staff (up a hundred and sixty-one per cent).

Okay, look. Those numbers are absolutely meaningless out of context. Used to tip a dime, now tip a quarter? That's a hundred and fifty percent increase. Also, the sentence itself reveals that "we" (not me) have always tipped assistant sports coaches (WHY) and theater staff, because if those started from a baseline of 0, there's no way to express an increase from that baseline as a percentage.

I've long ragged about lots of things TNY does. Publishing long-winded, pretentious articles. Promoting a dense, meandering writing style (I've called it The New Yorker School of Not Gettiing to the Fucking Point). Even adhering to anachronistic style standards, such as hyphenating teen-age or using diareses. But one thing I've always appreciated (besides the comics, which I've always found rather amusing) is their facts. Until this article.

It's not just the math thing, either.

The gratuity, classically, functions as a “thank-you,” but it can also serve as a “sorry.” People most often tip in settings where the workers are less happy than the customers. The Freudian Ernest Dichter once described the compulsion as “the need to pay, psychologically, for the guilt involved in the unequal relationship.”

Pretty much everything Freud proposed has been shown to be wrong. Consequently, I'm not going to take his followers' statements at face value, either, not without evidence. Also, I've never felt guilt (except on those rare occasions when I realize later that I should have tipped, but didn't). No, when I leave a tip, it's out of perceived obligation and/or generosity.

Michael Lynn, a marketing professor at Cornell, has studied tips for forty years, beginning when he was a bartender in graduate school. “When you think about it, you go, ‘Why would people give up money they don’t have to?’ ” In restaurants, he has found, the answer has to do with social approval.

Why would you give a gift to another person or to a charity? You don't have to. You'd have more money if you didn't.

English coffeehouses were said to set out urns inscribed with “To Insure Promptitude.” Customers tossed in coins. Eventually, the inscription was shortened to “TIP.”

This is the bit that pissed me off the most, though. And yes, I've ranted about this before, but no one listened. The word "tip" did not start out as an acronym. It's much older than the wordification of acronyms. The idea that it did is a false etymology, what I call a fauxtymology because while I hate other peoples' portmanteaux, I'm overly fond of my own. It's been thoroughly, completely, and definitively debunked,

and anyone who still believes it has absolutely no business claiming to be an expert on tipping, or writing a book about it.

And The New Yorker should be ashamed of itself for letting that get published. Shame. Shame. If I had a rolled-up newspaper, I'd bop them on the nose for it.

Incidentally, "for unlawful carnal knowledge" and "ship high in transit" are also fauxtymologies.

After that wholehearted nonsense, I couldn't trust any other assertions in the article. Might still be worth reading, but I doubt it's going to change any minds. Personally, I'd like to see tipping go away entirely, replaced by decent wages and bonuses like other workers get. But unless that happens (which it won't in my lifetime), we're stuck with it.

Which doesn't mean we have to give in to tip-beggars in traditionally non-tipped positions.

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