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 31, 2008 at 1:11pm

#627051

Eve

New Year's gives an opportunity to reflect and project. I've spent the last few days in relative solitude, but I haven't found answers (mostly because I've been playing Fallout 3 instead of reflecting, projecting, writing, working, planning, sleeping, eating...)

Reflections

For me, 2008 sucked big, hairy, greasy, moldy donkey balls. Oh, there were breaks from the suck, but for the most part, vacuum.

Certainly, it could have been worse. It was worse for a lot of people, but I'm not that good at empathy, and they're not Me.

The economy went to shit, and took my company with it. Part of the hazards of doing business, it is. I take some comfort in knowing that had I been working for someone else, I'd have been laid off, most likely, long before now. As it is, my company barely made money; hence, I barely made money.

I spent most of the year in severe pain. This is better now, but it's not great. I don't know if it'll ever be great again.

Dad got sick and then died, and I've been having to deal with the resulting paperwork ever since.

I still haven't been published.

On the bright side (every silver lining has a cloud, you know), I have great friends, both here and in the "real" world, and I'm still married, and I don't have any kids to complicate things further.

And really, I have everything that I need, so why should I bitch about this other stuff?

Projections

I'm going to go WAY out on a limb here and say that 2009 will be a better year. I may end up a year from now eating those words, but for once I'm cautiously optimistic. It's not that the economy can't get worse - it can, and probably will. It's not that my back will magically get better - but at least I have some confidence that it won't get much worse. Of course, one's father can only die once, so that isn't going to happen again (Mom died back in '99).

So I'm asking myself, what do I want?

Do I want my company to do better? I don't know - that would mean more work, which goes against my basically lazy nature.

Do I want it to tank completely? I don't know - I like having money. The more money you have, the more money you CAN have, and it represents security against times when you're NOT making money. You know... like NOW.

Do I want my back pain to go away? Yes, but at what cost? Some people say to make it go away I'd have to have surgery, which means a period of recovery with even worse pain, and I've never been one to trade short-term downside for long-term upside.

Do I want to be published? Sometimes I think so. Other times I feel like it would lock me into something. I don't know. It's very confusing.

Do I want to be happy? That's too nebulous a goal. What would make me happy? I don't know.

What do I want?

I don't know, and that's the honest truth.

I want things to be automatic, so I don't have to work for them. Unrealistic.

I want to spend my days on a Caribbean beach, drinking rum and staring at the ocean. I imagine that would get old fast.

I want to keep the house I inherited from my father, the house where I (arguably) grew up. But the upkeep and taxes on that may be prohibitive.

I want to have better relationships with my wife and my friends. But I'm a geek - I don't know anything about human relationships. I'd rather play video games or design spreadsheets. Besides, that's like work.

I want to lose more weight, but the plain truth is I love to eat and derive great pleasure from it, and I find nothing wrong with pleasure.

I want to stop having these struggles with myself, to quit battling myself for every choice I have to make.

I want things to be better, but I don't have the first idea how to make them so.

Well.

I suppose it'll just have to happen by itself.

Happy New Year to all of you fine readers, and may all of your problems have easy solutions.

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