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 31, 2007 at 8:04pm

#545821

Observances

I've been getting the distinct impression that some of my latest blog entries have been met with something less than enthusiasm.

That's okay. Part of my late trend toward sporadic posting was the result of some self-examination - I do that sometimes, perhaps to a fault, but another thing I figured out was that I shouldn't be making apologies to anyone for what I am. For what I do, sometimes, sure, but to quote God and Popeye, "I am what I am."

I have a tendency to write to an audience. The "audience" here is the people who actively comment. I can see parts of you, there, glittering in the darkness like so many stars. But as the Universe seems to be composed primarily of dark matter, unseen and poorly understood, so is my audience, and all I can see is the occasional twinkling point.

It was easy for me to forget that I started journaling not to please an audience, but to - simply - write. I didn't start out to be funny, or philosophical, or provide links to fun diversions offsite. I found myself censoring myself, keeping back the most meaningful thoughts in fear that I would lose what little light I had.

But to what end? I don't have to have the most popular blog on the site. And I shouldn't be craving approval - hell, that's what I have Minions for. If I can't say something outright, well, I should be good enough at the craft of writing to talk around it and at least convey something about whatever's going on in my life.

So October comes to an end today. I almost said, "at last," but this month has flown by like a stealth jet in the night.

There's a tradition, an observance, I follow every year in October. I re-read A Night in the Lonesome October by Roger Zelazny. Each time, I find something else about it to like. Zelazny was one of my favorite authors in general; he died prematurely in 1994, October having been his last completed work (the book is also credited to macabre artist Gahan Wilson, who provided copious illustrations for it).

The book is narrated by a dog. The dog, Snuff, is the companion of Jack the Ripper, whose task it is to preserve the planet by preventing the forces of evil from opening a Door to the realm of the Elder Gods. The narrative borrows from all kinds of literary sources, including Frankenstein and Dracula as well as Sherlock Holmes and, obviously, the works of Lovecraft. It's set in late 19th century London, with all the atmosphere that implies. It's about the nature of life, love, friendship, and redemption; and it's funny and macabre and sad and uplifting all at the same time.

Just what you need in October. So, yes, that's where I took my handle from this month: Waltz in the Lonesome October.

On Halloween or, if you will, Samhain, in addition to dressing up in scary or silly costumes and making your dentist happy, do try to take a moment to reflect on what has gone before. Much has been made of the observances of this season concerning evil spirits, the last harvest, and, more recently, costuming and trick-or-treating, but one of the lesser-known aspects of Samhain was its function as a time of reflection. Those who died in the previous year are remembered and, also, those who are no longer with us, who made an impression upon us. Your grandmother, perhaps. A favorite teacher. The dog you had when you were a kid. A favorite author who left pieces of himself behind when he departed. Perhaps even your younger self, that part of you that may not have known as much, but had a particular wisdom that it might be good to recapture.

The leaves fall, the wind blows them across the deserted path. You take a minute to look back, your hair streaming past your face as you consider what was, and that which has brought you to this place. You can't go back there; you can only stand and watch the leaves slowly obscure the path - but you take a moment to look, to remember... to observe. And then, resolutely, you turn and face forward, into the biting wind, perhaps pulling your coat closer around you as you shiver from more than just the cold.

Blessed Samhain. May the Ancestors grant you all wisdom, and may you find what you seek in the coming cycle.

Such times are rare, such times are fleeting, but always bright when caught,
measured, hung, and later regarded in times of adversity,
there in the kinder halls of memory, against the flapping of the flames.
-Roger Zelazny,
A Night in the Lonesome October

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