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

February 10, 2009 at 7:12pm

#635119

Surgery

9. I'm not sure which of 7 or 8 hurt more, but I wouldn't want to repeat either.

I admit it - I'm a weenie when it comes to pain. I don't like it. I don't think it builds character (though it may reveal it, partially), and I don't think there's any honor in bearing it stoically. No, I'd rather bear pleasure stoically.

It is, of course, unlikely in the extreme that I would ever have to get another appendectomy. That doesn't mean I'd never be faced with abdominal surgery, of course. I'm fairly sure that the abdominal surgery complicated my back pain, because it messed up muscles that normally serve in adjunct to the back muscles. Thus, I don't want abdominal surgery.

It goes without saying that I don't want any more needles near my eye. Hell, I can't even wear contact lenses, I'm so freaked out by the idea of something touching my eyeball. Fortunately, I've always had decent vision, and haven't needed lenses or glasses - until the past three or four years, when 25 years of staring into a computer screen most of the day finally caught up with me.

Surgery is supposed to result in a brief period of pain that substitutes for a longer-term problem, but someone would have to convince me that the pain of the problem will exceed the pain of the surgery and recovery.

Incidentally, pain is not the reason I won't get a tattoo. The reason for that is that I want the freedom, always, to change.

That said, you know what would make me change my mind about surgery? Well, imagine a drug that, whenever your nerves started to register pain, rerouted the sensation to a different part of your nervous system; specifically, the part of your brain that registers pleasure. This would be better than morphine, more addictive than hydrocodone, and more dangerous than a tomb full of asps.

Because, see, a drug like that would get out on the black market. People would take it, and they'd register all their pain as pleasure.

But pain is the body's way of telling you that you're doing something wrong.

But such a drug would make a great science-fiction plot feature.

I see any of you using it, and I'm coming after you.

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