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

Stik to My Own Beat

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 wanderlust-words-in-motion

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 wanderlust-words-in-motion

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 Surprised

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 17, 2010 at 9:30pm

#708687

I can TOO be social.

In my ongoing effort to be less of a reclusive geek and on the theory that living well is the best revenge (for being dumped), I've been traveling and going out more, lately.

So, last weekend (it's been that long since I wrote in here), my friend and long-ago girlfriend, Nicole, asked me if I wanted to go to dinner at the Melting Pot with her, her kid, her sister, her sister's two kids, and their parents. N's the only one who lives around here; everyone else is visiting.

Now, I'd met N's parents before, when we were dating. You don't forget things like dinner at the Ritz Carlton in Boston. I always thought they were pretty cool, though N doesn't get along with them all that well. Never met the sister (Denise), but to hear N talk about her, I was expecting horns, hooves and scales.

That turned out not to be the case. In fact, she was pretty hot-looking, and, as is rare for me, we immediately clicked. She even appreciated my puns, which is rare.

Ended up ditching the kids at the parents' hotel, and I went with D and N to the local brew pub, where we watched a bluegrass band from one of the couches (the tables were full). So there I was, sitting between two sisters, my arms sprawled behind them, gathering Looks from passers-by.

It's the little things in life, you know?

My friend, Mike, who's renting from me for a few months, recently got himself a girlfriend, a girl he met who was working at a coffeehouse (direct quote from Mike from when he was hitting on her: "I haven't drank this much coffee in... well, ever"). So apparently this girl, Shawna (which earned a snicker from me, though Mike hasn't read my Outer Banks erotica stories featuring a girl named Shawna), is a "derby dame," someone who does roller derby.

Anyway... she told Mike that at a local club Saturday night (yesterday, not a week ago... do keep up), they were going to have...

get this, now...

Sexy Zombie Jello Wrestling.

Meaning: Girls (some from the derby, some not) dress and make themselves up as zombies, and wrestle. In a tub filled with Jello.

Part of me was appalled at this, which clearly sets back the feminist movement 50 years. The rest of me tied and gagged that part and left her in a dark room to contemplate her error, then went to the Sexy Zombie Jello Wrestling.

So last night, I watched scantily clad zombie women Jello-wrestling, and I finally got to meet Shawna (who had a cast on her arm and thus, sadly, didn't wrestle).

Then, today - I missed it, because it would have involved getting up at 7 am, which I don't do anymore for any reason short of catching an airplane to somewhere - they had a Zombie Run. This was a serious 5k run which people signed up for for some cause or other, but what they didn't know was that they'd be running...

...while being Pursued By Zombies.

This would have been good training for the inevitable zombie invasion, but as the zombies didn't have to run the entire 5K, they had a significant advantage as they lurched, well-rested, out of the crowd and grabbed the runners, who from that point on had to become zombies as well.

Brilliant. Fucking brilliant.

So I had brunch with Mike and Shawna today, and they told me of this event, and I almost wished I'd gotten up at 7 am.

Almost.

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