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

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

February 14, 2011 at 6:32pm

#717855

Doomsday

Say what you want about being single, but I'm going to say this:

Having nothing to be pressured into doing on Valentine's Day (VD) is a major, major relief.

The crap I said in last week's Comedy newsletter aside, sometimes I think VD was invented by some misandrist woman who is probably chuckling in her grave over the crap we XYs have to go through on VD.

It's like this: I've never, not even once, been involved with a woman who appreciated VD. And contrary to popular belief, I've dated a few women.

And yet, almost every year, one of two things happens:

Either 1) I do the roses, chocolate, and dinner out thing, or 2) I get broken up with just before my birthday, which is four days from now.

Look... girls... it's like this: If you're into VD, just frakking SAY SO. Don't pretend you're not just to see whether we're committed enough to do something ANYway, because men are a lot simpler than that. "Don't get me anything for VD" means, to us, "Don't get me anything for VD." End of line.

If you ARE into it, that's cool. I can do the flowers thing. I'd rather make you a nice home-cooked meal, but even there you won't be going out while some of your friends certainly will, so there's a dilemma too: Do something from my heart, based on a skill I actually have (cooking) or do something to conform with your friends so you can talk to them about it the next day. And going out always involves overpriced, lousy food and crappy service, when we could just as easily go out on another night and have a great time.

The whole thing sucks, for us. Sucks. And don't give me the "You'll get yours on Steak and Blowjob Day (March 14)," either, because I don't want anything for S&BJD (or wait - yes, I do; I'm just not going to TELL you and let you figure it out for yourself when I'm lying on the couch pointing at it with a big grin on my face).

I know it sounds like I'm ragging on women, here, and I'm sorry if it seems that way. It's not my intent. It's only Valentine's Day that's the target of my angst this night. I guess VD brings out the worst in all of us.

So, yeah. Glad I've got no pressure, for once, this year. I'm just going to go over to my friend Nicole's house; she's ordered some takeout and we're going to watch some anime with her kid.

Wait... Oh, shit... am I supposed to bring chocolate?

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