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

June 14, 2007 at 8:40pm

#515276

Evan essence

Huge chunks of Evan Almighty were filmed around here. For a while there, they were actually building an ark near Crozet , which was useful when we had some nasty rainstorms coming through here last year.

So tonight the local fancy renovated movie theatre held the Charlottesville premiere of Evan Almighty. My wife scored tickets to the event because she was involved in something related to it, so I got to go for free.

It's not a movie I wanted to see in the theatre, and probably would not have gone without the freebie. Still, with the opportunity to be at the premiere - well, call me a sucker for that sort of thing. I figured it'd be worth seeing just for the local scenery, which I never get tired of. The director was there, introducing the film, and a lot of the people in the audience had been extras (sadly, none of them were elephants, giraffes, or lions).

So, should you see the movie or save your money?

(Fear not, no spoilers here. Nothing you can't glean from the previews.)

First, let's talk about God.

Sometimes, I fancy myself a writer. A writer can be considered the God of his or her own story. The writer makes the decisions, sets everything up, and has sole discretion over the way things are. The reader can dislike the writer's decisions, but she can't argue with them - usually (present company and rate/review system excepted). The writer can be right or wrong, but she's always the writer.

Now, here's the thing - as soon as you put God in your story as a character, you have what I call the "infallible narrator." The writer can still be wrong, but God-the-character is always right. This is because, if God-the-character were ever wrong, she or he would lose all credibility as God and become someone who plays at being God.

So you have to handle God carefully if you write her into a story. Kevin Smith knew this on a basic level, and so his God in Dogma (which, spelled backwards, is Am God), played by Alanis Morissette, was mute.

The God of Evan Almighty, as with Bruce Almighty before it, was played by Morgan Freeman, and I have to say he does a kick-ass job as the Big Guy. Still, the importance of point of view can't be underestimated: God tells Evan to build an ark. We see God telling Evan to build an ark. We, the audience, are convinced the guy in the white suit is really God even before Evan is - thanks to a few shortcuts by the author. So we sympathize with Evan's plight, to some extent or another, because we know that God, in the context of the story, really did command him to build an ark.

But here's the thing - again, not giving away much here - with point of view: Anyone comes up to me and says, "God told me to do such-and-such," and I don't care what it is: kill their family, feed the homeless, build an ark, whatever - I won't believe them. So I have a lot of sympathy for the other characters as well. They haven't had "signs." They haven't had Morgan Freeman doing parlor tricks around them. The audience, I think, is supposed to believe that the supporting characters are supposed to accept it "on faith" that God spoke with Evan.

And that's where the movie fails, for me, as a movie. It was funny - funnier than I expected it to be, with the physical slapstick humor kept to a fairly small segment of the movie. The animals were cute. The plotline was - well, I've seen a lot worse. There were too many Messages in it, but that's related to my main point, which is that when you put God in a movie, or a story, you're cheating.

Now - this is not to say that you can't portray people believing in God, and the movie kind of starts out that way - people who have a simple faith in God, and who pray. Nothing inherently wrong with that.

It's when the one you're praying to shows up with piles of wood that you have to wonder.

The main message? Be kind to each other. Well, hell, I don't need a movie to tell me that.

Basically, it's a fun movie, not to be taken seriously - it doesn't take itself seriously - and better than I expected it to be.

And the scenery is awesome.

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