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

July 22, 2007 at 8:11pm

#522982

Literary Merit

Lorien

, commenting on us finding something else to obsess upon now that the last HP book is out: "Preferably something with literary merit."

While I agree with the sentiment to some extent - as good as Rowling is at capturing and engaging the reader, she's not the world's greatest writer (Richest, maybe, but the two are not synonyms) - I have issues with literary writing. Now, I'm not sure exactly how Lorien meant it, but to me,"literary merit" is code for "a dense, impenetrable force field of twisted allegory, obscure allusions, and other ways an author can demonstrate how clever she is without resorting to plot or characterization"

Ann Beattie is a great example of this. So is pretty much anything in The New Yorker (at least, it used to be that way - I haven't even tried to read that in a while). When I was younger and I picked up mags like that, and tried to read the stories, I found them dense, impenetrable and impossible to understand. I figured, "I'm a smart guy. One day, perhaps after college has warped my mind to a sufficient degree, I'll understand and appreciate the rarefied subtleties of literary fiction."

Well, here it is a quarter-century later. I'm still a smart guy, and I still find that sort of thing dense, impenetrable and impossible to understand. Granted, I took very few liberal arts courses in college - being an engineer and all - but I don't think I'm ignorant about writing.

As with a lot of modern art - an exhibit showing an overflowing trash can and a canvas painted red with a purple stripe down the middle come to mind - a lot of it is, as I mentioned above, artists (painters, sculptors, writers, whatever) having stopped trying to be accessible to ordinary people and merely trying to outdo each other using rules created BY the field FOR the field.

I shouldn't need a degree in art history to appreciate fine art. I shouldn't need a degree in literature to appreciate reading. And writers (I'll leave artists alone from now on, because this is writing.com and not deviantart.com) need to decide whether they're writing for other writers - or for general consumption.

If you're writing for other writers, hey, that's great. Don't expect to become rich, but then, that would be "selling out," wouldn't it? If you're writing for the general population, of course, don't expect to get rich doing that, either. I don't. I expect to get rich (well, at least earn enough to retire) doing engineering. You've as good a chance at winning the lottery, the only difference being that with writing there is some element of skill involved.

If you can string a sentence together, turn a few phrases, stand some clichés on their heads, create interesting characters, put them in interesting situations, and bribe a few publishers, you can get readers. Who cares if it's a rehashed plot? At least it's a plot. The romance industry makes a living cloning plots - or at least I've heard they do.

So... essence of rant: the same people who would rather find out what's going on in Paris Hilton than in Paris aren't going to read "literary" writings. They're going to read Stephen King and Patricia Cornwell - and J.K. Rowling, if they read at all. I'm not writing to impress professors and black-wearing, clove-smoking elitists*; I'm writing to (try to) impress guys in Ford pickup trucks and single mothers.

Not ragging on you, Lorien

- I agree with you to a point. It just ain't going to happen.

*Incidentally, I wear black and I used to smoke cloves.

Comment • View 7 comments

July 22, 2007 at 1:28am

#522837

And while we're at it...

There's a subset of people on the internet who like lolcats.

There's another subset of people on the internet who like to take quizzes.

At the intersection of these subsets, I present:

http://www.okcupid.com/tests/6348388576689378978/Which-Lolcat-Are-You-

In cyberspace, no one can hear you squee.

Comment • View 2 comments

July 22, 2007 at 12:57am

#522830

Eight Hours of My Life

So the postman knocks on the door and hands me my copy of Deathly Hallows, which Amazon had oh-so-kindly labeled as such right there on the packaging. "People have been stealing these from mailboxes," he explains. "Thought I'd see if you were home."

Someone's getting a tip this year.

I spent the next eight hours straight reading the thing. Right now some of you are going, "Eight hours?! That's slow! It took me four and a half!" Shut the fuck up, okay?

All I can say is, there were a few things that surprised me, and at least two major plot points that I had nailed on the head. Plus, the ending was pretty much exactly what I expected - before I saw the god-be-damned Internet spoiler brigade. Did this disappoint me? Far from it. Just as with the ending to The Dark Tower, the prediction coming to fruition increased my enjoyment.

Sadly, however, Snape does not take McGonnagal to the dungeons.

And boy, am I glad that series is over. Move along, folks - let's all find something else to obsess upon.

Comment • View 6 comments

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