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

February 8, 2008 at 5:26pm

#566345

Comedy

Looks like I'm scheduled to do next week's Comedy newsletter. I was at a loss as to what to do, since there's not much room for comedy in my life right now, until I realized: it's coming out right around Singles Awareness day, and if that's not a theme ripe for exploitation, I don't know what is.

They say when you're at low points in your life, that's when you need humor the most. I guess I'm not at a real low point yet, but I have been twisted every which way this week, between finances and work and my dad being sent to the emergency room. He's pretty much stabilized now, but when a 90 year old man gets sent to the ER, it's rarely a laughing matter.

It made me realize that there's a few things I need to take care of, like making sure I know all his life insurance documents, military service information and so on. There are also issues related to his estate. And of course, thinking about all this has gotten me thinking about my own impending doom (which will probably be after his, but there are no guarantees except taxes and... well, you know) and how unprepared I am for it. I mean, no one is ever prepared for it, but I haven't even made out a will or advance medical directive or anything. Hell, I haven't even decided whether they should play Dark Side of the Moon or Darkness on the Edge of Town at my funeral yet. Maybe Pink Floyd for the funeral and Springsteen for the wake. Yeah, that'll do.

That, and I have a birthday coming up too, just a few days after Singles Awareness Day. One year for V-Day, my wife got some roses for me, painted them black, and had them delivered to my office. Now, THAT was funny. No colors anymore; I want them to turn black. This year, she wants to have our single friends over for Singles Awareness Day, but I don't think she's put as much effort into planning my massive, gala birthday party (at which I want them to play Dark Side of the Moon and Darkness on the Edge of Town and maybe some Zeppelin to cap it off) as she has into planning V-Day.

My birthdays have been crappy, anyway, since I turned 7 and my grandmother died the next day. She's buried in New York, where my mother joined her about a quarter-century later. They're in the same graveyard as Andy Kaufman (if, that is, Andy Kaufman was actually buried.) My dad doesn't want to be interred there, though. He wants to be buried at Arlington, alongside a million other veterans. I guess he wasn't much of an Andy Kaufman fan.

Well, I've managed to cover birth, life, love and death all in one short blog entry, and I've even given myself ideas for next week's Comedy newsletter. Guess it's not such a bad week, after all.

"There is no dark side of the moon really. Matter of fact it's all dark."

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