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

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.

1 Like

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

October 4, 2010 at 11:36pm

#707682

Costume

I need a Halloween costume idea.

I don't usually "dress up" for Halloween. I'm not a creative person (at least when it comes to costumes; I like to think my writing shows some vague glimmers of creativity) and so the extent of my outfits thus far involve me wearing regular clothes while carrying a box of Cheerios with a knife through it.

Puns, I can do.

See, okay, here's what's going on:

Saturday night, I was feeling depressed - it is, after all, October, and the days are getting shorter and I can feel my serotonin drying up like spit in the Mojave - so I decided if I'm going to be depressed, goddammit, I'm going to be depressed with a beer in my hand. So I went off to Beer Run with my Kindle, sat outside, and drank.

The cool thing about a Kindle - if there is one - is that when people see you reading it, they're all like, "Is that a Kindle?" Which surprises me, because Amazon has claimed since they first came out that they were selling like lemonade in the aforementioned Mojave. Which should mean that by now, FIVE freaking years later, everyone in the country ought to have two of them.

And yet, other than mine, I've seen... three.

Okay, anyway, so people were coming up to me going "Is that a Kindle?" None of them were cute, so I was just like "Yeah."

"How do you like it?"

I'd shrug. "It's like reading a book, only no one can see what you're reading."

Then my favorite waitress - off-duty that night - sits down at the next table with a dude who also works there and they order a beer.

"Hey, man," says the off-duty waiter (the waitress barely acknowledged my existence). "What are you reading?"

So much for not having the title on display.

Well, I wasn't reading anything embarrassing like "Hello Kitty Meets Edward Cullen and They Have Lots of Unicorn Rainbow Vampire Kittens," so I say, "Something by Jim Butcher."

He squints.

"Jim Butcher? Dresden Files? But this is his fantasy series."

Blank look.

By now I'd thought everyone had at least heard of Harry Dresden. I guess you have to have a Kindle.

About then my friend Mike shows up, saving me from further conversation with the desperately unenlightened. At the same time, Cute Waitress shows up with an Even Cuter Friend and they sit down at the next table.

Cute Waitress clinks glasses with fucking Mike. Bastard.

Anyway, they end up telling us that the National Zoo up in DC is going to have a costume party along with a concert by Grace Potter and the Nocturnals (one of those musical artists you've never heard of that I really like) and that they were going.

I consider the prospect of what kind of costume Even Cuter Friend might come up with, and make an on the spot decision that I was going to the party.

"Who's Grace Potter?" asks Mike, which surprises me, because he's even more into music than I am - but then, I'd had to teach him about Dar

Williams, so okay.

So Cute Friend explains - in terms of a lot of those musical artists that you've never heard of that I really like.

Suddenly, Even Cuter Friend became Even

Cuter

Friend. I'm a sucker for people who share some of my taste in music, okay?

Then I find out she's 21.

Goddammitalltofuckinghell. I finally meet someone who not only has heard of the artists I like but loves them, and she's less than half my age.

I have about as much chance as spit in the desert.

I still wanna go to the party at the zoo.

So I need a costume idea.

No sparkly vampires, creepy mouthless cats, or unicorns, please.

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