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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🌝 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.

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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

November 22, 2007 at 6:18pm

#550939

Getting Through Turkeyday

Let me preface this by emphasizing that I like my in-laws, and I'm not just saying that because my wife reads this. I honestly do like to be around them.

The problem is when they all get together on Thanksgiving.

There are three traditions that seem to dominate on Thanksgiving Day here in the US: A turkey dinner (which is actually eaten at lunch by most people), the Macy's Thanksgiving Day Parade in NYC (which is what's on TV), and football (American football, which is distinct from what we call "soccer.")

Of those, the only thing I can stomach is the turkey dinner. Wine helps. Wine also helps to deal with the other two things. I couldn't even allow myself to glimpse the parade for fear of beholding the Hello Kitty balloon.

There were 13 people there today (which I hope isn't some weird psychic reference to the Last Supper), and the bulk of the conversation was centered around the upcoming UVA vs. Virginia Tech football game. I'm a UVA grad; my wife went to Tech (as did my business partner, though she is into football, but of course she wasn't there). Meanwhile, some pro football game was on television. Oh, they also talked about hunting (which I don't do). My one attempt to talk about Springsteen was short-lived; there was one other fan there, and she was glad that the concert fell on her birthday.

I would have been bored silly were it not for the wine, and my brother-in-law.

He's not into football, either (nor is my wife). So while the others all sat in rapt attention before the Altar of Sports, Erik and I came up with the one thing that would make us want to watch football:

The Womens' Football League.

Now, in spite of some of the references I've made here in the past, I'm all for equality. And every other sport, up to and including rasslin', has a womens' equivalent - why not football?

Even knowing in advance the general build of the women who would be involved in such sport, I think it's hot. There would have to be a few changes made, though.

-The Quarterback would be called the Rebate (get it? quarter back?)
-The Line of Scrimmage would be termed the Line of Discrimination.
-There would not be "downs," but "tries."
-There would not be "quarters," but "periods."
-The goal line would be called the Glass Ceiling.
-There would be team names like the Amazons, the Shoppers and the Mace.
-The cheerleaders would all be gay men.
-The Blitz would be retermed The Half-Off Sale.
-It wouldn't be a Hail Mary pass, but a Hail Joseph pass.

There were a lot more, but I had rather a lot of wine and I don't remember much. I think once my wife caught on to what we were doing, she started laughing and writing them down - all three of us were laughing our fool heads off, earning us puzzled looks from the gathered family - though I think if her brother hadn't been involved she'd have dismissed my idea as being sexist.

Okay, so some of those terms are sexist, though I don't particularly care. But I think the WFL is an idea whose time has come. Equality for all!

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