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

May 20, 2008 at 9:24pm

#586193

Speaking of Screwing up the World...

...just in case you haven't noticed, this is an election year in the US.

Ideally, this would mean thoughtful debate about the positions and goals of each of the candidates, and sober reflection on which can best serve the nation as it currently stands.

But, as I believe Rita Mae Brown put it, "If life made sense, men would ride sidesaddle."

(Okay, that comment is even funnier if you know her, but you get the idea.)

Instead, we're treated to endless streams of criticism about who said what, and how that reflects on the candidates' ability to be elected.

Like we can't figure out for ourselves who can be elected.

Oh, well, maybe that's a good point.

Really, I don't recall the country being this polarized in my youth. Maybe I just wasn't paying as much attention then, but it seems to me the chasm between "liberal" and "conservative" (both of which are now misnomers) has widened, leaving those of us who harbor views from each extreme hanging. It's become a battle of absolutes. "Conservatives" are convinced that only they are right, and that they are for (e.g.) small government and less government interference in daily life (so why are they so against government interference in who can get married?) "Liberals" are equally convinced of their superiority, though examples elude me now.

Point is - well, even CNN was calling it "Ballot Bowl 2008." Like it's a football game or something, with the outcome decided with one clear winner and one clear loser, and winner take all, and what's the long-term meaning? Nothing, just like it matters not one iota which team wins a sporting event.

Well, sports are about the worst analogy I can think of for politics. You don't just wear one candidate's colors and start shaking your pom-poms (though it's interesting to note that G.W. Bush was a cheerleader in college). Sports is about winning, and playing fair (in that order). Politics should be about choosing the best course for the country - NOT what's best for any one individual, say the voter for example.

Democracy isn't there to cater to the whimsies and fads of a majority; it's there to protect the rights of everyone, majority or minority. When I hear that so-and-so wouldn't vote for Clinton because she's a woman, or Obama because he's "black" (he's half-white; how come he's not "white?"), I start to have serious doubts about the direction we're going. Because black, white, man, woman - none of that matters, really, if a society is fair and just.

Whoever gets the White House in November has some serious messes to clean up, and I don't wish that on anybody. But let's not forget the truly important thing: whoever it will be, it won't be Bush.

And that'll be cause for celebration.

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