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 8, 2008 at 3:49pm

#611826

Never ends

Up until a week and a half ago, I had that nasty, unrelenting back pain and sciatica, the only relief for which was lying down and taking lots of meds.

I was okay for a week, then. I mean, I still had twinges in my back and leg, but nothing major.

Then, as I reported here, I got sick on Sunday, cutting short our anniversary celebration. This continued through Monday.

Monday night, I slept for a few hours, then was wide awake for a few hours, until maybe 15 minutes before my alarm went off. When I woke up, my neck and shoulders were stiff. No big deal, except my stomach was still upset, so I went to work. I left work early afternoon, figuring what I needed was to lie down with some heat on my neck.

So I heated up a neck thing and went to lie down, and pain exploded between my shoulder blades such as made the worst pain I experienced with my lower back (not to mention appendicitis) seem like a pleasant day in the Caribbean.

I couldn't move. Oh, I could move my legs and, to some extent, my arms, but I couldn't sit up or roll over. I couldn't even play dead because I kept looking for a position that minimized the pain.

My mobile phone was not nearby, so I couldn't reach it to call anyone. Every time I tried, I felt like someone was pushing a knife into my upper spine.

I think I dozed off for a while. My phone rang. I had no way to get to it. I could only hope that my wife would come home before she went out to dance practice.

Fortunately, she did. Unfortunately, she had no way of moving me. Fortunately, one of our close friends is a chiropractor. Unfortunately, the chiropractor was still at work. Fortunately, we were able to leave a message. Unfortunately, the ditzbrain who took the message didn't give it to her. Fortunately, I called her mobile phone an hour later to see if she got the message. Unfortunately, she hadn't. Fortunately, she was still able to come over and fix it so I could at least stand up - albeit with intense pain.

Once I stood up, holding my head straight and not twisting or raising an arm, I was okay. We got back to the chiropractic clinic and she worked on me some more on the table. Then she said I couldn't get on the computer, so I sat with ice on my upper back.

Last night, I managed to sleep; this morning, I was able to get up on my own.

Still hurts like a bitch if I move the wrong way.

And I haven't really eaten anything in over 24 hours - my stomach's still rebellious.

But I'm alive.

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