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

February 7, 2007 at 7:40pm

#486430

Browbeaten

I appreciated yesterday's insightful comments about my Chekov entry. What I might have failed to make clear is that I actually did enjoy the story - it's just that as a person on this site who's gotten (and given!) many reviews warning against long expositions and adverbitis, it struck me as odd that an acknowledged master could get away with such things - successfully.

Sheherazade

mentioned translation and, yes, it did occur to me that some of my issues could be put down to translation.

Mavis Moog

brings up a good point about style police.

Here's the thing for me: I do not have classical literature training. By that, I mean I was exposed to Shakespeare, Faulkner and Hawthorne same as anyone, but never pursued much beyond AP English class. In college I placed out of English requirements, and concentrated on engineering (though I did have a fiction writing class, even then). So I don't KNOW what those techniques are that Mavis talks about; I only know when reading something whether I liked it or not - and very rarely exactly why.

I have, however, been reading science fiction since I was eight, and my writing - even that which is not SF - probably reflects it. While SF has been attaining greater literary heights lately, it's very aware of its roots as lowbrow pulp fiction.

Which brings me to esprit

's link to Twain on Cooper.

http://users.telerama.com/~joseph/cooper/cooper.html

I've always loved Clemens' writing. When I was a kid, I kept re-reading Tom Sawyer because it alternately made me laugh and be scared. His literary style alone does that. I laughed my damn head off reading the article.

Twain / Clemens wasn't writing highbrow fiction; he was, for the most part, writing for the masses - and the masses are notoriously lowbrow (come on; we're talking about people who watch Springer and American Idol here). But he wasn't lowbrow himself. He knew what he was doing, what effect every word he put down would have. I don't think Twain would have given two shits what a professor thought of his work - at least, that's the impression one gets from his writing.

Impression, of course, is key.

I'm not writing for professors; I'm writing for your average person. I don't write for kids; I write for adults, even when I'm not writing erotica. If I am ever successful, it will be because my works are popular, not because some professor is entranced by my cleverness.

But to do that, I have to be clever - in a subtle way.

I'll let you know if I ever figure that out.

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