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.

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

January 3, 2010 at 10:13pm

#682283

The Light that Never Warms

Today, I told myself, I would finally get some work done on a story I want to submit to a magazine. Goal, remember?

Naturally, I kept putting it off, finding other stuff to do that brought me more immediate satisfaction , and now it's after 10 and I have to go back to dreary work tomorrow.

I swear I don't know why I do this to myself. It's like there's something inside of me telling me I shouldn't even be trying, to be content with what I have.

I am content with what I have. I just want something else, too.

Is that so goddamn wrong?

I'm going to go buy a ping-pong paddle to use on my inner brat.

Bastard.

Tomorrow, then. No excuses.

(Yeah, right, like that'll happen.)

*Kick* Ow!

Comment • View 6 comments

January 2, 2010 at 12:47pm

#682107

I like to think I can be so willed

Today marked my first visit to the gym of 2010, as I spent most of yesterday sleeping and writing.

Now, I didn't go to the gym much in December because I spent most of the month sick (and the rest drunk). But before that, I was going pretty regularly: Body Pump 1-2 times a week, yoga 1-2 times a week, and the occasional trip just to get on an elliptical and cuss out Fox "News." The gym is pretty much right between home and work, 10 minute trip either way, max, so I can't use inconvenience as an excuse.

Unfortunately, the entire town seems to have made a stupid New Year's Resolution. Finding a parking spot was the least of my problems, though that took a lot of energy by itself. Every goddamn machine they had was taken, so I didn't even bother and just went to yoga class - which was so crammed full of bodies (mostly guys, unfortunately) that we couldn't even do some of the... whatevers. Asanas, I guess.

(On the other hand, the more people you have going "Om," the cooler it sounds.)

But what the hell, right? I expected this. I couldn't NOT expect it. But that doesn't mean I'm not going to bitch about it. If you go back to my "Goals" post, do you see anything there about being more positive, less cynical, more accepting, less bitchy? No. At least I can make it funny.

I figure it'll be this way until about my birthday, and I'll just have to visit the machines during off-hours, like mid-morning or mid-afternoon, and get to classes early enough so I can get all the equipment.

And if that fails, there's always putting on sweats and running around my neighborhood. At least that way I can make the neighbors laugh, too.

Comment • View 5 comments

January 1, 2010 at 5:04am

#681929

All Your Sanity and Wits, They Will All Vanish...

...I promise. It's just a matter of time.

As New Year's Eves go, I've done a whole lot worse than rocking out to Gogol Bordello live.

They started at about 10:45 and played until maybe 12:30. At midnight, they did the mandatory countdown thing and then launched into "Start Wearing Purple" - so I got to start out the new decade on a high note.

About the only thing I can think of that could possibly top that would be a New Year's Eve Springsteen concert.

Like that's going to happen.

I've come to the conclusion that there's really not much I can rely on. Cats die; people avoid you or leave; writing is fickle at best; work is subject to the vagaries of the economy; sleep is elusive; money provides some security but no comfort; bodies wear out and leave you gasping for breath; cars break down at the worst times.

But music -- music is always there.

I talked about goals in my last entry, but my mission is to have more music in my life.

Oh, and more comedy, too. Since Sophy

mentioned my blog in her last Comedy newsletter as a source of laughter, I guess I'd better stay funny.

And so I present to you a New Year's joke I found somewhere (hey, these things can't really be copyrighted anyway):

On New Year's Eve, a woman stood up in a crowded pub and said that it was time to get ready. At the stroke of midnight, she wanted every husband to be standing next to the one person who made his life worth living.

As the clock struck twelve, the bartender was almost crushed to death.

*raises half-empty glass* Here's to life!

Comment • View 2 comments

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