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 13, 2008 at 6:55pm

#596206

Speaking of journalism...

Speaking of journalism, as I might have mentioned before, my friend Pat works for the local newspaper. By "local newspaper," I mean the traditional daily paper with sections and legal notices and available for $0.50 in vending machines across the city.

The other newspapers in town are weeklies, and they're free, so those are the ones I actually read. Sometimes.

Thing is, like I said in yesterday's entry, I'm pretty sure journalism is dying, even as its domain is largely being transferred from print to online media. I threw out the "I blame bloggers" line as a self-deprecating joke, but I may be more serious than I thought.

See, there's an old saying to the effect of "Opinions are like assholes; everyone has one, and most of them stink." Back in the old days, if you wanted to express an opinion publicly, you had to send it to the aforementioned newspaper (or one of its ilk in a different town) along with your name and address and other identifying information, and they'd verify that it was you before they printed it - so you don't go impersonating someone you don't like, I guess.

Now, of course, we're pretty much all anonymous and we all have our own opinion pages where we can shout out any old thing. No one checks the facts, and if someone has an objection it's likely they'll just quit reading, and stick to sources they agree with - or, at worst, send a comment like "U SUCK!!!1!"

Anyway, Pat's paper just laid off its entire printing press staff. Seems rather than pay to fix the press, they're just going to send the pages over to the next town, and have it printed there. They'll cart the papers back here for distribution.

I don't know if subscription rates are dropping; I know I dropped mine as soon as I got an internet connection.

There's more to the death of news than just the impending death of print media, though. For starters, there's no longer any need to polish a story before it goes to print; you can just print what you have and post an update later. If something turns out to be offensive, you can delete it. And it pays to post a first draft; after all, they still want to scoop the other guys.

So we're left with three different, but interacting trends:

1) Everyone's a journalist, and there are fewer and fewer editors or ombudsmen.
2) Print media is dying, and
3) Internet sources are questionable.

Journalists have every reason to be lazy.

And as orangefiire commented on my last entry, I'd rather hear the raw truth on the news than a bunch of government entwined crap that's on there. I suppose for the individual journalist without any sense of morals, being aligned with the gov't makes their life easier - and makes us all more ignorant. Well, whether aligned with the government or not, everyone has an agenda. Hopefully that agenda is, "I will present the facts." But usually even that is affected by some bias. Conservatives are always whining that the media has a liberal bias, so they purposely lean right in their own spaces (like Faux News). It's hard to write objectively when all the facts run contrary to your predetermined point of view.

Well, I think reality has a liberal bias, but what does my opinion matter?

I have an agenda, too - it's to make myself utterly irresistible to all women and eventually take over the world. I think I'm succeeding.

Since my other agenda is also to be funny (actually, that works toward my main agenda), I'll link this relevant quote, found for me by my friend elleetwombly:

http://www.overheardinnewyork.com/archives/000211.html

20-something Intellectual: Facts are such a distraction from the essence of what's really happening.

Pretty much sums it up, doesn't it?

By the way, hit "Random Quote" from that page - it's hours of funny.

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