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

December 7, 2007 at 10:15pm

#553953

A New Take on Why We're Fat

I get really, really tired of all the "news" articles that follow the format:

Our society has an obesity problem because *shakes Magic 8-Ball* there's too much sugar in our diets! (or too many fats, too much carbs, too much soda, too little self-restraint, or whatever)

But this one I'm about to link actually makes a good point. I've noticed for a long time that when I try to eat healthy, I end up broke and thinner, but when I don't give a damn my wallet and I both get fat. This article actually applies observational data and draws a somewhat scientific conclusion:

Calorie for calorie, junk foods not only cost less than fruits and vegetables, but junk food prices also are less likely to rise as a result of inflation.

http://well.blogs.nytimes.com/2007/12/05/a-high-price-for-healthy-food/?f=1

As I implied above, I'm getting sick of hearing about how fat we are as a society and the mad scramble to find excuses why. Me, I have very little self-control when it comes to food; but I've learned to live with that and am finding ways around the problem. It never helps that no one seems to be able to make up their minds about what's good for you and what isn't. It used to be meat that was the boogeyman; for a while, it was fats; then carbs; then it turns out that some carbs are okay, and, hey, some fats are okay - as long as they're not trans fats. Believe it or not, for a while there, eggs (I call them 'cackleberries') were seen as the root of all dietary evil.

I strongly suspect that a large fraction of the "studies" commissioned to find out what is and isn't good for you are bought and paid for by various special-interest groups. Like, vegetable growers might get a study done that says meat is bad for you. The wheat industry gets together and does a study that denounces fats. Crisco buys a study that says fats are just fine; but don't eat white bread. That sort of thing.

And I still don't understand why sodium compounds are supposed to be evil.

Anyway, if that article has any validity, we get to the root of the problem: simple economics.

Now excuse me while I go eat a bag of pretzels.

Comment • View 5 comments

December 7, 2007 at 4:19pm

#553906

Further Proof...

...that the world is utterly, irrevocably whacked.

Okay, actually it's proof that the people in the world that are utterly whacked. I mean, I was wrong: it's not just Brazil after all.

http://www.techcrunch.com/2007/12/03/yahoo-top-searches-2007-please-people-stop-...

Really, the headline says everything that needs to be said: Please, People, Stop Typing Britney Spears Into Search Boxes

I'll say it again: FUCKING STOP TYPING BRITNEY SPEARS INTO SEARCH BOXES.

Typical conversation for me:

Them: "Did you see where Britney-"
Me: "SHUT UP! Who cares?"
Them: "..."

But Them's right, and I'm wrong. It's not "Who cares?" It's apparently, "Who doesn't care?"

Am I really the only person on the planet who's never typed "Britney Spears" into a search engine?

Emma Watson, sure...

Now on to #2: WWE.

WTF is WWE? I thought to myself. I've never heard of that, but if it comes up #2 on Yahoo! searches, maybe I'm missing something obvious, so... let's give that term just one more hit.

...Rasslin'?

Rasslin' gets more hits than Paris Hilton? I don't THINK so. And I mean that exactly how it sounds.

That takes care of 2 and 3, but what's that "Naruto" thing at #4? Again, I pander to popular culture by merely searching for it:

Ah. It's about a ninja. That's okay, then.

Then I got to #5 and my mind shut down, so I'll stop there.

Comment • View 8 comments

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