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:

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').

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.

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

1 Like

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

October 19, 2023 at 10:39am

#1057671

Crappily Ever After

I've been saying that every cliché started out as profound insight.

Before They Were Cliches: On the Origins of 8 Worn Out Idioms
Erin McCarthy and the Team at Mental Floss Examine Some Famous Phrases

While they call out Mental Floss, the above link is from LitHub.

Worn-out phrases can make a reader roll their eyes, or worse—give up on a book altogether.

"Roll their eyes" is itself a cliché.

Clichés are viewed as a sign of lazy writing, but they didn’t get to be that way overnight; many modern clichés read as fresh and evocative when they first appeared in print...

Which is what I've been trying to say.

But of course, many clichés are tired and worn-out, but they have to be used sometimes, or else how will people know when you subvert them or make a joke out of them?

Add Insult to Injury
The concept of adding insult to injury is at the heart of the fable “The Bald Man and the Fly.” In this story—which is alternately credited to the Greek fabulist Aesop or the Roman fabulist Phaedrus...

Look, if anything's that old and passed into cultural mythology, it's not a cliché; it's an allusion. Or just part of the language, like a word, only it's a phrase. Like "part and parcel" or "cease and desist." Though no one knew the origin of this phrase. Except us, now.

Albatross Around Your Neck
If you studied the Samuel Taylor Coleridge poem “The Rime of the Ancient Mariner” in English class...

We skipped that one, and I still haven't read it, but I haven't seen this phrase used enough to consider it cliché. Also, it's an allusion, too.

Forever and a Day
This exaggerated way of saying “a really long time” would have been considered poetic in the sixteenth century.

My nitpicky mind always thinks "but when time runs out, we have no way of knowing the length of a day."

Happily Ever After
This cliché ending line to countless fairy tales originated with The Decameron, penned by Italian writer Giovanni Boccaccio in the fourteenth century.

Okay, look, no. Used at the end of a fairy tale, it's not a cliché; it's a formula, the flip side of opening it with "Once upon a time." Other languages use different formulae. You might as well claim that "amen" at the end of a prayer is a cliché.

It Was a Dark and Stormy Night
Edward Bulwer-Lytton’s 1830 novel Paul Clifford opens with “It was a dark and stormy night.”

Oh, come ON. I thought this list was about overused phrases that were fresh and wondrous in the beginning, but this infamous story-opener was widely hailed as "bad" from the get-go. That's why it makes great comedy material.

There are a few more, but I'll be honest, here: Yesterday, I finally broke down and purchased Baldur's Gate 3. And I'm in a hurry to get back to gaming. So feel free to see for yourself; I don't have the same sort of commentary on the others, anyway.

4 Like • Comment • View 1 comment

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