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 9, 2008 at 4:47pm

#612014

FAILboat Now Departing at Dock 13

So today, the DJIA blows past 9,000, heading down to its close at about 8580. The S&P 500 index is flirting with 900.

One year ago today, the Dow closed at 14,165 - highest point ever.

What's that, like, a 40% drop? This is going to make the Great Depression look like a goth kid wannabe.

So let's get this straight: Banks fail, taking everyone else along with it like a sinking battleship drawing sailboats down in its whirlpool. Treasury and Fed both push for a "bailout" which really amounts to the printing of more money, practically guaranteed to hike up inflation. I'm still not entirely sure how that was supposed to help, but I thought it was supposed to help the economy, keep it from going bust, and we HAD to have it RIGHT NOW or things would go straight to hell. THEN they cut the lending rate by 50 basis points, practically guaranteed to encourage banks to borrow from the gov't instead of each other. And things are going straight to hell.

Now, I'm just an engineer, and I don't know squat about high finance, but to me that would be like noticing the skyscraper you just built has silly putty for the foundations, and replacing said silly putty with Astroglide.

We all could use some Astroglide right about now, I think.

Oh, the markets will recover. Hell, I wish I had more free cash lying around right now to mop up the blood in these here streets. Is this as low as it can go? No, it's not. What you're looking at here is called "deleveraging," where a whole lot of money that was in the stock market didn't really exist because it was borrowed - either through margin, short selling, or just plain borrowing and then investing.

There's a whole lot of money out there that doesn't really exist, you know. That's how the system works. I just wish I had more of that nonexistent money.

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