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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Turkey DrumStik

about an hour ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

a day 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

a day 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

February 11, 2019 at 12:35am

#951705

Rules for Writing

And now, folks, it's time for the February round of Bullshit Or Not!

https://lithub.com/jonathan-franzens-10-rules-for-novelists/

Now, this is a short article, so I'm not going to paste it here. Because that would violate Rule #0: Don't Plagiarize. (It's okay to borrow. It's even more okay to steal. It's never okay to plagiarize.) So please, read the link (as noted, it is very short).

First test of bullshit: who the hell is Jonathan Franzen?

Won awards: Okay.

Wrote for The New Yorker: Christ. I hate that mag.

Conclusion: writes for writers, not for readers.

Also, look at the picture. Look at it. "Okay, we need to make it clear that you're a writer, not a military officer, line cook, or assembly-line worker." All he's lacking is a pipe and a crystal decanter of Scotch.

Consequently, anything he has to say is probably erudite as fuck, but that doesn't mean it'll be useful. I mean, if you want to drive a car, do you pay more attention to what drivers say, or what automobile engineers say? I mean, okay, probably a little of both, but when it comes to the practicality of driving a car, I want someone with experience driving, not someone with an intimate knowledge of torque ratios.

On top of which, the linked article is really just an ad for his book. As such, it fails miserably - for me, anyway.

So here's my take on the Rules:

1. So what?
2. Writing for money is a good thing. Because money is a good thing.
3. This... okay, I can agree with this.
4. "Irresistibly?" There are reasons to write in different points of view. Choose the most appropriate one. Avoid present tense.
5. When the information that is universally accessible is of questionable provenance, finding the actual facts is a valuable thing.
6. Literary-genre authors like to proclaim that paradoxes make sense.
7. Dafuq does that supposed to mean?
8. It is doubtful that most people are writing good fiction.
9. Unless you find books like Jim Butcher's Dresden Files series interesting, I'm uninterested in your opinion on writing.
10. Again with the impenetrable pronouncements. "I need a #10 here. How can I appear profound? I know; I'll throw in something about love."

Now, I know, I know, this guy is published and I'm not, so maybe he knows what he's talking about. But if you can't figure out what he's actually saying, so what? It's torque ratios when I need to know how to start the engine.

So, what do y'all think? Bullshit... or not?

3 Like • Comment • View 3 comments

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