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

October 14, 2008 at 7:20pm

#612874

Market Down

Because I've talked about financial matters, people have asked me stuff about the stock market.

I am not an expert in the stock market.

My father was an excellent investor. I wish I'd listened more to what he had to say about it when he was alive and in possession of his faculties, but isn't that the case for most of us? In any event, I'm not my father, but like many people, I have a retirement account. And as with many people, mine's down about 40% right now.

Now, a lot of people are panicking. I may not know much, but I know this: as much as I joke around here about the end of the world, doom, Armageddon, Ragnarok, etc., I don't really think we're there. We won't even be there if McCain gets elected (though if he should become incapacitated and Palin ascends to the demigoddesshood that accompanies the Presidency, it may be another story). This is just another belch in the digestive tract of the world markets.

Which is not to say there isn't more pain to come. For myself, the pain may be acute, because my business depends on a thriving building industry, and that's just not happening yet, not in my area. But it's still not the end of the world. Well, provided I can still drink.

At some point (I don't know when, and neither does anyone else), the stock market - and the economy - will recover.

What I do know about investing can be summed up in a few general rules. I made ten of them, since that seems to be the traditional number:

1. Don't panic.

2. Minimize your debt (preferably, just mortgage).

3. Stay invested in the stock market, either through mutual funds or a diversified portfolio of individual stocks.

4. Don't invest with money you'll need in the next few years (if all your investments are in a retirement account, and you're not going to retire soon, that fits the bill).

5. Keep a cash position that'll get you through lean times (most people recommend 3-6 months' living expenses) in an insured bank account.

6. When you DO invest, look for stocks that are cheap in relation to their value. If you don't know what that means, get a mutual fund or buy into an index fund.

7. Keep expenses down so you can invest MORE.

8. Pay no attention to stock analysts, and completely ignore Jim Cramer.

9. Don't trade in and out of the market.

10. See Rule #1.

Drinking is optional, but it helps.

If you've made it this far, and you want to know more about this sort of thing, the best place I know to learn about personal finance is http://www.fool.com/

And now to try to drink again...

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