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

March 26, 2007 at 6:04pm

#497778

Debt is Bad, mmmkay?

It's been a while since I've ranted about fiscal responsibility, and then I read this article today:

http://www.alternet.org/workplace/49676/

The federal government -- and the majority of Americans -- can no longer get by a single day without taking on additional debt. ... Eventually the higher levels of debt will lead to higher interest rates, which will lead to more debt, creating a cycle as vicious as it is inevitable.

I've heard doomsayers before. Most of the time, they're wrong. This time, though...

We're all building a house of glass cards, here. It might blow down, or it might shatter, or both. It is painfully obvious to me that this situation cannot continue for very long.

Inevitably, there will be finger pointing. There is already finger pointing with the mortgage situation. The Federal Reserve is being blamed for allowing the situation. The banks are blamed for providing subprime loans. People are being blamed for defaulting on them. Well, this latter has some basis in reality - they're the ones who signed the papers, and it's their own fault if they don't read the Ferengi print.

Ultimately, I see a society where desires turn into wants, and wants turn into needs, and needs are purchased on ever-expanding credit. Advertisers con us into needing things we never even knew we wanted, and we eat it up. Hell, half the people I know who watched the Superbowl didn't give a crap who was playing; they just wanted to see the commercials.

The idea that someone might watch television for the sole purpose of viewing the advertisements is so alien to me it might as well be someone telling me I really ought to try shoving my arm into a meat grinder, just for the experience.

There have to be alternatives to debt. Some of them might not be pleasant to contemplate - they involve things like living communally, going without certain things, and driving less than 100% reliable cars, and no one wants to hear that.

"Oh, but I need to have a brand-new car." "You've obviously never had hospital bills." "I just can't live with a roommate." I've never heard such absolutism as I hear from people who are in debt up to their ears. [I know I talked about "needing" a stereo in my ride in my last entry, but you'll note I still haven't done anything about it.]

Do I have debt? Yes. I owe money on my house, and I owe money for the business. Both loans are secured by real estate collateral. I don't have a car loan. I don't have credit card debt (I use a credit card for everything, and I pay it in full every month, on time). I have no student loans. Have I been in worse debt? Hell, yes; that's why I feel so strongly about it now. I'm not perfect; I don't have the retirement savings that I should, nor all the insurance normally recommended. And now I'm starting to think I don't have enough hedge against the coming doom.

Before you ask, no, I don't make a shitload of money. I make more than some, less than others - my personal income is below average for my age, and so is my wife's. It's not about what you make; it's about what you spend. And while I admit to many areas in my life in which I'm "lucky," there's no element of chance in this; I chose to have a small debt footprint. Anyone can do this. It takes time, patience, discipline. Less than it takes to lose weight, though - at least for me. More than it takes to quit smoking; again, personal experience.

It won't be enough to ride out the coming apocalypse, though - when the economy collapses, my income stream dries up. That's why I'm preaching. I couldn't give a crap if everyone else has debt, as long as it doesn't affect ME.

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