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.

1 Like

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

April 24, 2009 at 9:34pm

#646779

RavenCon

First, thanks to all of you who commented on my last entry - I appreciate the thoughts.

In spite of the death of my little cat, or perhaps because of it, I still went to a convention this weekend. RavenCon, in Richmond, not as long a trek as the other con I went to. But this time, I'm without my wife - this con doesn't feature drumming or bellydancing, which along with vampires might be the only thing to drag her to one of these geeky things. I'm not enough, that's for sure.

One of the reasons I'm here is one of my favorite webcomic cartoonists is here. This guy:

http://www.somethingpositive.net/

Which I've mentioned before, but if you're new: it's helpful to click on the "First Comic" link on that site. If you're horrified, disgusted, offended, or anything but amused at the first comic, don't bother reading the rest. I, of course, found it hilarious.

Anyway, I haven't seen Randy yet, though I stopped by his table (someone else was staffing it) and saw his amusing line of t-shirts, also visible through links on the site above. I met him once before, last time he came to Richmond. Hopefully, he doesn't remember me. I'd become a bit inebriated, and was at a table full of fellow geeks, and we were trying to out-Monty Python each other.

What I did do is go to a writing workshop. The weekend is awash in them, and I hope to visit more tomorrow. The concept of tonight's workshop was characterization, which I was interested in because I threw away a line in my last Fantasy newsletter to the effect of the importance of creating memorable characters.

Of course, character descriptions are pretty useless on their own - except to the author. Chances are nobody wants to read your raw notes about a character (unless perhaps they're a writer interested in the process), any more than they want you to spend the first 100 pages of your fantasy novel rewriting the Book of Genesis for the world you created.

So the exercise was to a) create a character, quickly but fleshed out in terms of age, basic background, etc. and b) write a REALLY quick scene where the character meets a hooded female figure on a balcony, and must stop her from doing... something (undefined, and not to be explicitly stated). This effectively takes a character created with no idea what story s/he's going to be in and putting the character into an unfamiliar situation.

What I wrote (hastily, remember) was:

The door slid shut behind me, muting the clamor of voices. Dark clouds brushed most of a moon. I stood still, my gaze sifting through the shadows.

Where was she? She had to be there.

A break in the clouds, a glint of silver, and as if she knew she was revealed, she stepped forward, her face hidden in the hood.

But it was her.

"Ill met by moonlight," I told her.

"You shouldn't have come." Her words were ice.

"I had no choice." I stayed by the door.

"You always have choice."

I got points for referencing Shakespeare, and I think the panel liked my word choices (I've been working on favoring action verbs over linking verbs), but what I really got out of this was:

1) Know your characters.

2) Character is not about what happens to you, but what you do about it.

3) I really need to get back to writing SOME kind of fiction EVERY day. (Blog entries don't count.)

Something's always getting in the way of 3, but I need to do something about it. You know, to reveal my own character - or, perhaps, change it.

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