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

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

August 1, 2007 at 5:34pm

#525187

Alone in the Dark

My wife's taking off for a week, starting tomorrow, to go to a massive camping event with lots of bellydance workshops, leaving me to sit at home, alone, in the dark...

Wait, that's my habitat as it is.

As she's camping, she didn't want to have to bring her usual wedding/engagement ring combination, for fear of losing it / getting it stolen / it getting in the way. So I went to a jewelry store to get an alternative wedding band.

Well, actually, first we both thought that a puzzle ring would be cool.

http://www.puzzlering.com/

But there wasn't enough time to special order the kind she wanted. Maybe for our upcoming fifth anniversary, if I still have money then.

So anyway, I go to the jewelry store to get this alternative ring. I knew it should have some kind of stones, but I was hoping for maybe rubies or something else, something other than diamonds. Each diamond contains drops of blood from the slaves who wrested it from the cold, hard earth. Okay, I don't really care about that - the rock on her engagement ring is huge - I just like saying that.

I found a suitable ring, and didn't have to hock my business to buy it, but Kirstin's fingers are skinnier than most - which usually only serves to make the enormous rock on her engagement ring seem even bigger. The ring I found had a total of 1/2 carat of sweatshop diamonds inset in a channel setting. Naturally, the store would have to send it out for resizing - which might take two weeks, when she had to leave sooner than that.

Fortunately, we found a local jeweler who did it for forty bucks, but had to pull out and reset two of the slave-blood misery diamonds, and I hope her fingers don't shrink any, because the jeweler said the ring won't get any smaller.

So now all the guys at this camping event will know she's married. Whether they'll care or not is another story. Maybe I should have bought a chastity belt instead. Don't get me wrong - I trust my wife. I just don't trust other men - mainly because if I saw her, I'd try to pick her up without bothering to look at her finger. Oh yeah, that's how we met in the first place.

She gets a week of crappy showers, belly dancing and either dust or mud. I get a week of being able to leave my empties lying around, the bed unmade and the toilet seat up. I also get to finally watch movies I can't when she's around, like Kill Bill and Pink Floyd's The Wall.

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