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.

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 25, 2007 at 9:24pm

#497593

Not Optional Equipment

Yesterday was another "Drive around Virginia in my old pickup truck whose radio is broken" day. Having spent the last few weeks driving only from my house to my office and back, and little else besides, I hadn't been pushed to get the stereo fixed.

Yesterday, though, was the last straw. I borrowed my wife's boombox for the trip. (When she uses something of mine, it's not "borrowing," but it is when I use something of hers. Fortunately, I rarely want to "borrow" her clothes.) I grabbed the CDs that I made from the absolute best songs of my playlist, got in the truck and took off...

And discovered that the boombox won't play my CDs.

Shit.

I was able to tune in to a radio station sometimes on the box, but the land between Charlottesville and Fredericksburg is notably lacking in radio. Oh, there was some country stations, and some guy telling me all about Jesus (as if I'd never heard of Jesus in all my 41 years). When I did pick up something decent, it faded in and out every time I passed a large concentration of metal, such as a car, mailbox or Civil War battlefield (each of which is about as common as the others on this trip).

Sadly, I was running on a deadline, or I'd have stopped in Fredericksburg to pick up a new boombox, one which my wife could then take and maybe let me borrow it from time to time. Well, actually, I did stop, because Fredericksburg has become so choked with traffic that it makes the Long Island Expressway look like, well, an expressway.

But that was nothing compared to the trip back. Route 1 in Stafford County, going south into Fredericksburg, was backed up for - I'm not kidding or exaggerating here; I've driven that stretch enough to know - Five Fucking Miles.

I figured, wow, there must be some kind of accident up ahead. Occasionally, there'd be a car coming north, laughing at us poor fools in the southbound lanes. But as I inched - tunelessly - along down the road, it dawned on me that the source of the backup was...

The Falmouth light.

Yep, one single intersection - the one where Route 1 and Route 17 business converge - backed up traffic for five miles.

And they ask me why I don't live near Fredericksburg anymore.

Now, as it was Saturday, ordinarily this would have been at worst a minor annoyance. I wanted to be home, sure, but I could have dealt with it. If, that is, I had some tunes.

No. Instead, periodically, some snippet of the worst possible tune would come into my head. I don't even remember now, nor want to, what it was. Something from a commercial, or something. Or maybe it was some tune I knew when I was a kid, because that area would bring back memories like that - it was the route my parents used to drive me on to kindergarten. Hell, it might have been "if you're happy and you know it, clap your hands" - but then, if it were, you'd be reading about me in the paper right now instead of in my blog.

Today I went to Crutchfield, only to discover (though this didn't surprise me) that they don't have stereo people on Sundays.

Tomorrow, though. And I don't care if I have to take time off work to do it.

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