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:

🌖 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

Stik to My Own Beat

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 wanderlust-words-in-motion

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 wanderlust-words-in-motion

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 Surprised

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 17, 2012 at 12:05pm

#751157

Doomed.

We're doomed.

We're alone in an uncaring, unfeeling universe.

Wait... let me back up and I'll explain how I came to this inevitable conclusion.

One of the blogs I follow is called English Russia. I want to visit Russia someday, so I find the stuff fascinating.

Usually, that is. Sometimes, though, you get something like this:

http://englishrussia.com/2012/04/16/hey-is-she-real/

I mean, go look at that. Really. It appears that this Russian chick has done... things... to her face and body that make her look like some kind of living Barbie.

There's a concept used in video game and animation design called the "uncanny valley." You've probably heard of it. If you haven't, here's the Wikipedia page:

http://en.wikipedia.org/wiki/Uncanny_valley

To summarize, if a robot or animation looks almost, but not quite, human, we react more negatively to them than if they look like, I don't know, R2D2 or something.

What we have in the Russia link above is, apparently, a human female who dips into the uncanny valley from the other end. Either that, or Russia is poised to take over the world with its army of fembots.

As I realized this, I remembered that Japan had made almost-realistic fembots, and so I made the grave error of Googling "Japanese fembot." Shut up; I had SafeSearch on. It wasn't hentai that made me realize we're doomed. What I did find makes hentai seem safe, even comforting, by comparison.

It was this: (safe for work if not sanity)

http://www.techfresh.net/lovely-actroid-der2-fembot/

Three things went through my mind within the first microsecond of looking at that link:

1) Holy shit, it looks more human than the Russian chick.
2) What? Sanrio did that? The same company who has unleashed the Nefarious Neko upon a helpless world?
3) Wait... that means that they can now create an army of Hello Kitties that will TAKE OVER THE WORLD.

Doomed.

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