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 8, 2008 at 10:50pm

#595381

As you wish.

susanL

sez: Okay okay, your links are educational and funny and outragious. I like em all right. Just write too, deal?!?

Be careful what you wish for.

I spent my evening thus:

4:30-6:00 I went home and napped. I don't sleep well at night. I sleep better during the day. I prefer sleeping in the morning and waking up at the crack of noon. Since I work, however, I have to get up at around 7:30.

Well, actually, I have my alarm set for something like 7:00, and I hit the snooze button until I simply can't, anymore, and finally get my ass out of bed.

This is true no matter what time I went to bed the night before. It could be 9:00, 10:00, 11:00, or freaking 3 am. I just plain can't get up when the alarm goes off.

I never will understand the people who smugly get up at first light - or even before - and then treat it like it's some sort of moral superiority. Check this: It isn't. Not ever. It's simply a lifestyle choice, and my lifestyle choice is to get up between 9 am and noon.

So the early bird catches the worm? So what? I don't like worms, and the second mouse gets the cheese. MMMMMMMM. Cheese.

Where was I? Oh, yeah. This leaves me exhausted most of the day, and I usually want a nap when I get home.

6:00 - 8:00 There's this subdivision plan I did when I worked for someone else, as opposed to working directly for clients with my own company. It happens to be located within a mile of my office, about 2 miles from my house. It wasn't built according to plan - not the end of the world, but now the new homeowners are experiencing drainage problems. I don't like having my name on a set of plans where the homeowners have problems; it's rude. So I went out and met with one of the homeowners, a heart surgeon at UVA Hospital.

Now, I decided to be a civil engineer instead of a doctor because when I make mistakes, generally, people don't die. Except when there's water in their basements and they get that nasty black mold.

Well, nobody's died yet, but I know about water in your basement. I've lost a lot because of water problems, including a first-pressing Cold Spring Harbor album by Billy Joel, complete with Alvin and the Chipmunks voice. susanL

knows what I'm talking about.

So I met with this guy for two freaking hours while trying to figure out how to make the drainage work so it doesn't get into this guy's basement - and being a heart surgeon, he probably has stuff even more valuable than mine. But he's not a civil engineer, so there I was.

8:00 - 10:00 I sat on my back deck, drank an entire bottle of Vouvray, and talked to a friend of mine on the phone who used to be on this site. She put up with this shit. A saint, she is. Hopefully, when my wife comes home, she'll put up with it, too.

See, like I said, most of the time when I do something professionally, if I make a mistake, no one dies. When it's made clear to me that this is not necessarily the case, I don't care to face the resulting responsibility. Now, the particular situation was more a matter of the contractor not following the plans - but still, my name's on the plans, and that's what people will see when digging into records.

The only rational solution is to drink, really.

10:00 - ? Nicely pickled, I sign on to find this in my gmail inbox:

http://www.zeitgeistmovie.com/main.htm

Which is currently playing in the background, and freaking me out, even though I can identify certain mythological and symbolic errors made by the narrators. But it includes a bit by George Carlin which I've always liked. The damn thing is over 2 hours long, and I'm just in the mood to watch - or at least listen to in another window - the whole thing.

And then I find the above comment to my last blog entry, and now, aren't you glad I actually wrote something and only included 3 links?

Oh yeah, the other two links.

http://blog.wired.com/cars/2008/07/tesla-motors-ha.html

Tesla Finally Hires Someone Who Knows What He's Doing

Tesla Motors has hired one of Detroit's sharpest engineers to spearhead development of the four-door electric sedan it says will be rolling off an assembly line by the end of 2010.

Long-time readers will recognize Tesla Motors as the architects of my dream car.

http://www.teslamotors.com/

It's electric, and there's no way for me to get one right now, but as a middle-aged man, I claim this as my mid-life crisis car.

Want.

Really, really want.

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