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.

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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.

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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.

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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
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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.

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October 31, 2022 at 12:01am

#1040005

Eh? Okay.

When it comes to words, "correct" is a bit ambiguous.

Which one is correct: O.K., OK, ok, or okay?

Or should that read: "korrect" is a bit ambiguous?

In honor of the 182nd anniversary of the first-ever appearance in print of O.K. (in The Boston Morning Post) I am here to start an internet copyediting war.

Said anniversary was apparently last year, as this article dates from March 2021.

Also, "an internet copyediting war?" Right, like anything actually gets copyedited on the internet.

As you can see, the original “O.K.” was very clearly an acronym, in this case of “oll korrect,” a popular slang misspelling of “all correct” (we can probably blame this on the teens of the era).

Lest anyone think that teens making up expressions to piss off their stodgy elders is a new phenomenon.

As with most language that drifts into common usage, the origins of O.K. slowly receded from collective awareness and the word began to assume different shapes and sizes: the slightly more streamlined and dashing OK; the drawling and onomatopoetic okay; the abrupt and minimalist ok. (Who knows, maybe mmmkay will achieve formal status one day.)

And yes, the "oll korrect" origin story is disputed,

though that seems to be the leading hypothesis.

What's not in dispute is that it was made up at some point. All words were; it's just a matter of how long ago.

So what is a copyeditor to do? One of the best pieces of advice I ever got was from an old alt-weekly copyeditor at a bar, who didn’t really prescribe to this fixed style or that, but rather believed first and foremost in the “ugly rule.”

In truth, I'm pretty sure most style rules are the result of copyeditors going to bars. One thing I think most of them would agree on, though, drunk or sober, is that this author should have either used "...prescribe this fixed style or that..." or "...subscribe to this fixed style or that..." The way it's written makes no linguistic sense.

He held (correctly) that language and its rules are slippery and ever-changing, and that convention and usage should always supersede institutional formality.

While this may be "korrect," there's still no excuse for mixing up its and it's; there, their, and they're; or prescribe and subscribe.

So, within that admittedly wild and wooly ethos he came up with the Ugly Rule, which privileges the reader’s eye above all else, and seeks to minimize typographical distractions (in practical terms, the New Yorker’s truly eccentric insistence on diacritics is a direct and egregious violation of the rule).

Which is what I've been saying.

Whether it should be "wooly" or "woolly" is also up for debate.

He also believed that words, over time, tended to shed their size: compound hyphens disappeared, capitalization faded, and spaces closed up. Hence to-day became today, Band-Aid became band-aid, and (thank god) Web site is becoming website; and if these contractions were inevitable, why not just get in early?

They're not inevitable. But it is the way trends go in English. I've done entire blog entries on the phenomenon. Here's one that coincidentally (or is it ironically?) riffs off a New Yorker article: "Dashing"

Can you see where I’m going with this?

I can, but don't you get paid by the word?

This is why, as an editor, I prefer ok to OK or okay. Why fight it? Why waste the extra ink?

What ink?

The problem with ok is that it looks like it should be pronounced with one syllable, similar to oak or ach. The problem with O.K. is that it's absolutely archaic; hardly anyone puts periods into acronyms or abbreviations these days. OK is a decent compromise, but okay is closest to how the "word" is actually pronounced.

Full disclosure: I'm pretty sure I use them all interchangeably, but I think I lean more towards "okay."

I also had to go and look up some "texting rules" post I made several years ago, because I had a vague memory of being told not to use "k" for "okay." Here it is: "Unwritten, Expanded"

The important excerpt: "So... wait... we're supposed to, on the one hand, condense our texts into emojis and "u" for "you" and acronyms such as IDK or LOL or whatevs, but you're going to get pissed because someone typed "K" for "OK?" Good gods."

So, in conclusion, this author doesn't actually answer the headline question. My personal opinion? Look at how The New Yorker handles it, and do whatever they don't.

That'll be okay.

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