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.

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.

June 9, 2022 at 12:04am

#1033638

Got Me Doing It

Entry #3 for June's "Journalistic Intentions"

[18+]

Got Me Doing It

This one has a remarkably short description for a TVTropes page, but I can distill it even further: One character has some kind of manner of speech or habit, and another ends up unconsciously copying it.

From what I've seen, and glancing at some of the examples, this is usually comedy. It doesn't quite fit the Played For Laughs

trope because it's not a parody of a serious plot device. But the point is it's normally intended to elicit at least a smile or a sensible chuckle from the audience. And as we all know, or should know anyway, the wall between comedy and tragedy is paper-thin, and one often hears the other having loud orgasms in the next room.

I just came up with that, and I'm quite proud of it.

Where was I? Oh, yeah. So I can see it being drama too, is the point, if it's framed right.

But there's a third choice. Someone's probably already done it, but I can't be arsed to read all the examples on the linked page, nor can I remember any instances of it. And that third choice is using your weird mannerisms to do good.

That page I just linked is also about using one's powers to do evil, but using this one to do evil would still be comedy. As apes, we're very, very good at aping, so if one of us does something creative or slightly "off," others can pick up on that and, under the right circumstances, mimic it. The expression is "monkey see, monkey do," but monkeys aren't apes. We are. This is often called something like "leading by example." Under the right circumstances, your good deed will be contagious.

A real-life example of this would be a phenomenon I've heard of but never experienced because I almost never go there and never through the drive-thru: the "pay it forward" (PIF) conga line at a Starsucks. Coincidentally, I'd just heard yesterday of another one of those happening. With all the inflation going on, my comedian mind immediately went to "each order will be more expensive than the last," meaning that every customer would pay an ever-increasing tab.

And then, naturally, I thought of how I could use that power for evil. To do so, I'd have to work in an office or have a bunch of friends, but hey, I'm a writer, so I can imagine impossible things. What you do is, if you know there's a PIF line at the Starsucks drive-thru, you get in the line and order like 60 venti espresso soy milk double-shot cocoa mocha lattes (or whatever the goddamn stupid trendy drink is these days) and all of their danishes. Then the person in front of you is morally obligated to pay for your $5800.00 order instead of her $6.50 single short Tazo herbal tea, which the person in front of her had to pay for. And then you only have to pay for the Grande Americano of the idiot behind you.

Of course, I would never actually do such a thing, because you might get some goody two-shoes hero working there who warns the lady in front of you that you ordered everything in the store, and then you're on the hook for the $6300 bill (it went up while you were waiting for the order to fill). Because I consider it my hobby to think about everything that can go wrong with a scenario. That's an important skill for a writer to have, you know.

Normally, I only use the power for good.

Normally.

4 Like • Comment • View 3 comments

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