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.

1 Like

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!

2 Like

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

May 6, 2008 at 6:49pm

#583669

Dreams and Secrets

Because of its inclusion on a list for a reviewing group, my story "Dreams and Secrets"

has been getting a lot of feedback, lately.

I wrote it nearly two years ago, now. Since then, I've written... well, very little, apart from blogging. I keep getting story ideas, and sometimes writing them down, but that part of me, the part that got me onto this site, has been - not exactly shut down, but spinning gears.

I've long felt that a writer is someone who has to write, like de Sade in Quills. And I just haven't had that push, lately.

That story I referenced above - it's pretty obviously my attempt to write in the style of Neil Gaiman, one of my favorite authors. From the feedback I've been getting, I think the attempt was largely successful, in that it seems to elicit the feelings I was going for, and leaves many readers wanting more.

The thing I have to wonder is: Is there more? It's the prologue, not to a novel or story, but to an idea of a story, and not one that I've fleshed out even in my own mind. I get caught up in symbolism and metaphor, and I can't find a plot that works.

I'm sure you've read stories, or poems, that try to capture the feeling of dreams. I have, of course, by Neil Gaiman and by others, but to me, none of them come close. I've come close, now, with two stories: that one and another, older story. But can another author capture, for an individual, what that individual's dreams feel like?

Am I so different that the feel of my dreams is different, or is it just monumentally difficult to capture that feeling, to put it into words? It's not the same feeling as you get with movies with excellent special effects, even Neil Gaiman's Mirrormask.

Why would you want to? Because dreaming is a common human experience, like love and death, and to relate to other humans you have to invoke your common experiences; to use common languages like dreams and love and death to convey something that is, perhaps, outside a reader's experience. A translation, of sorts.

Besides, I see my job as a writer to affect a reader's emotions, to make him or her laugh, or cry, or be outraged - and sometimes I almost feel as if I can.

Almost.

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