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 2 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 4 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.

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.

August 2, 2021 at 12:16am

#1014867

Pronoun Pronouncement

Sometimes I even make blog entries about (gasp!) writing. (No, despite the title of this entry, it's not about listing your pronouns in your bio.)

It’s time to talk about “It’s”
It’s overused. It’s lazy. It’s something that should be stopped.

Everyone has their little annoyances. And in this case, the annoyance is, indeed, little.

“It’s” is a linguistic plague that is affecting all publications.

“It’s” is lackadaisical writing.

You know, when I first found this post, I felt myself filled with trepidation: Will this be one of those linguistic anarchists who insists that life would be better if we eliminated the apostrophe so that certain ignorant writers could stop getting dinged for mixing up the possessive and the contraction?

Fortunately, or unfortunately (because I had a whole rant prepared in my head), no. It's about using "It's" grammatically, but overusing it.

Funny thing about pointing out annoyances in writing: once you see them, you can't unsee them. Like when people use too many "-ly" adverbs in a story. So by harping on the overuse of "it's," the author overuses "it's," in a transparent attempt to get us all to hate it, too.

It’s time that I show you some examples of ledes (journospeak for the first paragraph of an article) that begin with “It’s,” which I have quickly cherry-picked from various publications excluding the New Yorker because I am out of free articles.

Whew. I've railed on the unnecessarily pretentious, precious, preternatural, purple prose of The New Yorker before (most notably here: "Antiphony"

) and I really wasn't in the mood for an example from them tonight.

Anyway, I won't recopy the examples here. The link is up there for a reason.

Many different words describe these ledes: Passive. Lethargic. Stultifying. Boring-ass.

I mean, passive, yeah, but not in the sense of "passive voice." I'd argue that the problem with most of them isn't the word "it's" by itself, but that they're dense with linking "to be" verbs in general, of which "it's" isn't even the most egregious example. Take the first one (like I said, you'll have to go to the link): It's, we're, were (though to be fair, that last one indicates past continuous tense). Replace at least one of those with an active verb and you get a whole lot less stifling scene-setting.

But now that she's inundated us with "it's" examples, we can't help but feel some of her pain.

This brings me to another pervasive trend: The sad abuse of present tense.

Present tense is standard for headlines, which is why every headline now is “X is x.” It’s all very meta which, fine. Life is recursive. But more enervating is how this convention is used in ledes.

I'm on the fence about the "it's" thing, but I'm firmly in the author's camp on this bit.

Headlines have been present-tense for a long, long time. I can't be arsed to delve into the entire history of newspapers, but here's one I found with a quick search,

from 1953: "Everest is Conquered." Which perfectly fits the format today's author noted (which, incidentally, should have been "X is y" unless she's actually talking about something like "A dog is a dog," or some other tautology, which I see only rarely, let alone "every headline").

I generally despise present tense writing, other than in headlines. Or jokes. Or certain other exceptions, but the point is, it's overused for everything from feature-length articles to entire fucking novels, and it's wearying. I get that using present tense conveys a sense of breathless immediacy, but for me it paradoxically brings me out of the moment. It's a gimmick to try to keep the attention of people with tiny attention spans. But I have a tiny attention span, and I still get more immersed in a past-tense novel.

Other people seem to like it, of course, but some people also think eggplant is food, so there's no accounting for taste.

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