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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🌝 HuntersMoon

Sep 20, 2025 at 12:12am
In response to "Numbers End"

Boy, am I behind thee times. I thought you just put this on hiatus. Of course, in March I wasn't a complete devotee of your brilliance yet.

I'm more than happy with Carrion Luggage, however.

1 Like

Elisa, Snowman Stik

May 1, 2025 at 7:09pm
In response to "Shhhhhhh"

Anytime I hear/read about the Quiet Zone, I am always reminded of this video.

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:16pm
In response to "Penultimatum"

As my Grandmother used to say, "Everything changes except that which stays the same." I never did understand why she said it, but it sounds good.

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TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:13pm
In response to "Numbers End"

Looking forward to the new book and hoping you don't encounter a meteor.

1 Like

Lazy Writer est 4/24/2008

Mar 12, 2025 at 4:19pm
In response to "Numbers End"

Sorry this one is closing..I will look for the new one tomorrow! Looking forward to it.

2 Like

Aiva Raine

Mar 12, 2025 at 3:45pm
In response to "Numbers End"

Thanks for a great 3000 entries.

Looking forward to the new blog, whatever it might be.

2 Like

Wordsmitty ✍️

Mar 12, 2025 at 1:36pm
In response to "Numbers End"

OK. What have you done with the real Robert Waltz?

Also, for the scientist engineer in me, have you actually tried to make entry 3001 and been rejected. Until there's proof, it's not real.

Thank you for your indulgence and sharing of wisdom.

R.I.P. "Complex Numbers"

3 Like

Anni Pon

Mar 12, 2025 at 11:20am
In response to "Numbers End"

Sorry that this one is coming to an end, but I'm excited to see what you have in store for the new one!

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Wordsmitty ✍️

Mar 11, 2025 at 1:42pm
In response to "Penultimatum"

It's been an enlightening run. We wish you well in your next adventure.

It will be interesting to see if after the next entry that WDC actually does stop you from adding another.

We're all waiting on pens and pencils for the unveiling of the new blog and to discover what it will be called.

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BIG BAD WOLF is Merry

Mar 11, 2025 at 10:46am
In response to "Penultimatum"

I'm reminded of this scene from The Princess Bride.

(Vizzini has just cut the rope The Dread Pirate Roberts is climbing up)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means.

3 Like

January 9, 2007 at 12:14pm

#480168

Fifty Five Thousand Six Hundred

I don't know why I didn't figure this out before, but I just realized that if I'm successful in completing this month's "Daily Writing Challenge"

[E] (Level 3), I will have written 55,600 words related to that activity by the end of the month. That's more than a standard NaNoWriMo attempt.

Of course, it is by no means certain that I will be successful. Yes, I know that's self-defeating. I'm just like that these days: I go through the motions, but I don't really expect to succeed. This may be because when I expect to succeed, and don't, I become angry or depressed. On the other hand, when I expect to fail, and I succeed, it feels okay.

That many words mean little by themselves. But I'm trying to keep a kind of narrative theme going. Is it a novel? No, probably not. There's not much conflict, no villains (yet), and it's more of a framing story for other stories I'm writing - the writing of which I really need to get back to, but the framing story is captivating. To me, that is; maybe not to readers.

Which leads me back to wondering why I bother. Am I getting anything out of it? Sure, the knowledge that I can write that many semi-coherent words. And actually, I'm figuring some stuff out about description, characterization, and dialogue - even if they're negative examples. Maybe a few GPs.

Why am I saying all this? I'm not really looking for encouragement or further discouragement or advice, though I'd accept them. Some people have been encouraging me to try to get stuff published. I'm not sure why I'm still resistant to this idea; maybe because writing, to me, is easier than all the stuff I'd have to go through to send in manuscripts, make contacts, and so on; and more rewarding than collecting rejection slips. I appreciate the votes of confidence, but I guess I'm just not ready to stop being lazy and cynical.

I guess I need to settle on a direction and go in it. I have at least two science fiction stories, one urban fantasy story, and one horror story in this weird thing I call a head, just wating for me to get my shit together, outline them, and start writing. Actually, some of them, I've already started writing. All of them are at least novella-length.

I do know one thing. If I am successful in writing 55,600 words at the end of the month, I'm going to have a few good, stiff drinks. There's a commitment I know I can keep.

This boring, introspective journal entry has been brought to you by Not Enough Caffeine. We now return you to your regularly scheduled fluff.

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