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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Show Recent Comments

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

April 24, 2008 at 4:49pm

#581379

Movie!

Not to be one to yell "Movie!" in a crowded firehouse, I'd like to point out that this may just be the best year ever for movies.

Consider:

-Speed Racer
-Hulk
-Iron Man
-Indiana Jones
-A whole bunch I've forgotten.

Yep, this summer promises excellent lowbrow entertainment. Good guys, bad guys, explosions, and cars. What else could you want? Oh, yeah. Well, there'll probably be boobies also.

For those of you who may be unfamiliar with real entertainment, I give you:

http://www.cracked.com/article_16176_8-pointless-laws-all-comic-book-movies-foll...

8 (Pointless) Laws All Comic Book Movies Follow

Hollywood is a land of money and cowardice. Every big film is basically a $150 million gamble, so they tend to play it safe and stick to a successful formula.

Nowhere is this more evident than in the genre of big-budget superhero franchises, where it's been decided that you must follow most if not all of the eight rules below:

Comment • View 3 comments

April 18, 2008 at 2:47pm

#580102

E Street

One thing I haven't done much crowing about lately is Bruce. He's been touring, and quite successfully, with the E Street Band. I have tickets to a concert that's scheduled in just a couple of weeks, right here in my town, and I am excited about it even though it's just two days after my dad's funeral.

For the past few months of the tour, though, one E Street fixture has been missing: Danny Federici, organist and keyboardist. The press releases said he was "taking a leave of absence from the current Bruce Springsteen and the E Street Band tour to pursue treatment for melanoma."

Danny had been there longer than just about anyone - he was one of the original members of the band, and has worked with Bruce for almost as long as I've been alive.

I found out today that Danny died yesterday. He was 58.

Now, with my own father's death so recent, I'm not as smacked by this as I might be. After all, my only connection with this guy was enjoying his music for most of my life. So it's not like I'm going to wear black and mope about for the next week. (Well, actually, technically, I am going to wear black, because that's what I do anyway - it's slimming. But no moping.)

Still... it sucks. It makes me feel old, and contemplate my own mortality once again.

But, for those of you who have been reading my newsletters - I won't do next month's on death again.

Comment • View 3 comments

April 15, 2008 at 5:53pm

#579579

Counting by Tens

First, a nice collection of "rage against the machine":

We asked our readers to terminate their most offensive technology and submit the best photos of the destruction. After weeks of voting, these are the 10 top revenge photos from those who won't kowtow to our future overlords. [Funny, for a minute there I thought they were talking about the Chinese...]

http://www.wired.com/gadgets/miscellaneous/multimedia/2008/04/gallery_gadget_abu...

And from nice to naughty, a gallery of... well... you just have to see it to believe it. But only if you're 18 or over, Claire.

Rejoice! The week is at an end. You have worked hard and now it's high time you got to relax and enjoy a "Thank Giz It's Friday" roundup of gadgets that are pointless, vulgar, confusing and (in some cases) scary. If you find yourself saying "I have that!" a number of times while perusing the following gallery, it might be a good idea to sort some things out with a trained professional. [AKA "Waltz's Wish List"]

http://gizmodo.com/378756/10-sex-toys-that-are-confusing-and-wrong-nsfw

And finally, from what is fast overtaking fark.com as my favorite snark site ever:

10 Things That Pissed Me Off About CNN The Other Night

The other night I was watching Larry King Live. Why? I'm not sure. It probably had something to do with my testicle clamp being in the shop. Anyway, in less than a minute worth of show, I found no fewer than 10 people or things that pissed me off.

http://www.cracked.com/blog/2008/04/09/10-things-that-pissed-me-off-about-cnn-th...

Now let's see if it'll take me a week to find thirty more things to laugh at...

Comment • View 3 comments

April 10, 2008 at 5:17pm

#578726

Just so you know I'm around...

As writers, of course we're exhorted to avoid clichés like the plague. But you know, sometimes we just have to go with the flow. Well, here's some cliché origins you probably didn't want to know about, but you're going to click on anyway, just for the hell of it:

http://www.cracked.com/article_16108_bizarre-history-10-common-sayings.html

A lot of the English language seems to have been developed as some kind of elaborate practical joke. It's full of little sayings and idioms that on their face make no sense at all, and if traced back to their origins are downright horrifying.

Right or wrong, these 10 sayings have some of the strangest (and most unsettling) histories:

Of course, that reminds me of this little gem some anonymous poster on the internet said about the origins of English (edited to correct the ubiquitous anonymous-internet-poster misspellings):

"I always thought of English as the bastard child of an orgy of languages ending with a huge bukkake leaving German covered in the messy splooge of all the others. German is seeking a paternity test while Latin fled the scene and French is denying everything."

And I'll just leave you with that image...

Comment • View 5 comments

April 7, 2008 at 8:25pm

#578186

Family

My elderly aunts (not my dad's sisters, but my late mom's sisters) are going to come down for the funeral. They both live in New York City, so it's a fairly easy journey: bus to subway to train to subway, and they're at Arlington.

Of course, they have to complicate things by saying that's too complicated. "We'll come down Sunday," one said. "We'll stay in a hotel overnight and leave Monday after the funeral."

Which, of course, is still better than their Plan A. "We'll take the train. Can you pick us up at the Washington station?"

Sure, Aunt A., but do you really have to make me drive around DC (which, though I've done it more, is far, far worse than driving around NYC, and about on a par with driving in Boston, about which the less said, the better) on the day of my father's funeral? Sure, the train station isn't hard to get to, and it's a quick hop across the Potomac to Arlington, but what if I make a wrong turn and end up in Alexandria or Fairfax? Every time I get familiar with what passes for the road "system" in DC, they change it. I'd end up, potentially, late for my father's funeral. Fuck that.

So Plan B is better; I just have to find an inexpensive hotel for them in the DC/Arlington area, that they can get to by cab from the train station, and get a cab from there to the Cemetery.

Snicker. Snort. Yeah, right.

Comment • View 4 comments

April 6, 2008 at 8:20pm

#577967

Checkmate

Yeah, I know it's been a while. I didn't want to do this last week, because it was just too new to me, but now's the time, I suppose.

The title of this entry refers to a previous one, "Endgame"

.

A week ago today, Dad died peacefully in his bed. While I didn't get there in time, a very nice hospice nurse was there with him, so at least he didn't die alone - for whatever that's worth, insofar as all of us die alone. Unless we get blown up by a suicide bomber in a crowded mall, or somesuch.

Now, I want to die in bed, too, but what I mean by that is when I'm 95 or thereabouts I want to be shot in the head by a jealous husband.

His stated wish, from 'way before he began to feel the effects of Alzheimer's, was to be buried at Arlington National Cemetery. Part of what I was doing last week was trying to fulfill that wish; on Friday, I found out that it would happen. So, toward the end of the month, he'll be buried with full military honors in what might be the most famous cemetery in the world, alongside presidents and generals, but not near my mom, who's buried in New York.

So, that's it. Ninety and a half years of life, from New Orleans and several times around the world to come to rest in his adopted state of Virginia, not even fifty miles from the home he built.

I've got a newsletter to do, now. Comedy, this week. Yes, I can still laugh - how could I not? Then, later this week, I should be able to take care of some of my other obligations on the site, like the contest I'm supposed to be running. Life goes on, and I'm going to live it.

Comment • View 9 comments

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