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

June 6, 2007 at 6:46pm

#513538

Pirates

While in Floriduh last weekend, we saw Pirates of the Caribbean: At World's End - appropriately enough, considering we were maybe an hour from Disneyworld at the time.

When the second movie came out, I indicated that I wasn't impressed by it. Well, I was a bit more impressed by this third movie - the pirate accents were somewhat less thick, and I could understand most of what they said. The plot took enough turns to keep things interesting, and a lot gets wrapped up; there's not much more you can expect from the last of a trilogy.

Damn thing was long, though - and I hear they had to cut it even to get it to where it was.

But I've come to a broader conclusion than mere movie criticism:

I don't like pirates.

*waits while someone revives Problematic Content

*

No, I haven't turned into a ninja.

The movies are fun and all, but the more I think about it, the more I don't like the glorification of being a pirate. "Take what you can... give nothing back." Seems to me that such an attitude is the problem, not the solution.

In the same theater, on a previous visit, I saw Superman Returns when it came out, so I couldn't help contrasting Superman with the whole pirate thing. I got to thinking: Superman (not a ninja) is the polar opposite of a pirate. I'd expect his philosophy to be more on the lines of "Give what you can, take nothing back." Less fun? Maybe, but...

I keep running into people who are proud of how they scorn rules and such - the pirate way. Others claim to follow rules but don't - which is, admittedly, worse, because at least with the first group you know where you stand (with your hand firmly clenched around your wallet). Thing is, rules and laws and so forth were put there to help us get along with each other - something that becomes ever more important in a society where global communication is nearly instantaneous. At a time when we need to be more careful of other people, we're becoming less so.

Robert A. Heinlein once wrote (paraphrasing here) that the decline and fall of any civilization begins with a breakdown in interpersonal courtesy. I'm not really sure if he had facts to back this up - all civilizations fall eventually, and one culture's courtesy can be another culture's mortal insult - but I wouldn't be surprised if there were a correlation. But no - we find it "cool" to insult each other, especially in the safety of the basement of the Internet, and insults have been big business for a long time.

"So people need to stop being thin-skinned." The problem with developing a thick skin is that you lose sensitivity.

Even the fictional pirates had a code - today's "pirates" don't seem to have even that. They take what they can. They give nothing back - except the ubiquitous clever, rude insult.

Do I want to see things become more politically correct? Not I - far from it. There's a line, though, and most of us don't seem to know where that line is. Probably has something to do with the Monkeysphere I posted about a while back. Some people just don't register as people, not when there are six and a half billion of us crowding the planet.

"The world's a smaller place now"
"No - there's just less in it."

Comment • View 4 comments

June 6, 2007 at 12:18pm

#513464

Just Wrong, but funny

http://imgs.xkcd.com/comics/electromagnetic_spectrum.png

(You don't have to be a geek to get it - but it helps)

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