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

May 23, 2007 at 6:27pm

#510554

Bitching

I thought I should put the last entry into perspective.

Yes, having a cold is a pain in the ass. It's nasty and miserable, and the only thing keeping me smiling is the knowledge that I probably gave it to someone who deserves it more than I do.

I'm not really bitching about it, though. Just making a gross and, hopefully, funny (to someone) blog entry.

See, on Sunday I found out that my ex-wife is in the ICU at a local hospital. She's been diagnosed with an untreatable form of pneumonia, as well as an abscess in one of her lungs. Don't ask me how that happens. I don't know.

I can't even get in to see her because I've been, well, sickly, and one of us might infect the other. Not that it matters so much, because people who have gone in to see her have said that she's so knocked out on sedatives and such that she's completely unresponsive. Just lying there motionless, kind of like when she and I - no, not even I will go there now.

I'll let you all in on a little secret. Most of you know I've said some nasty things about my ex-wife here, and in my previous blog. It's too easy a target, ex-spouse jokes. The secret, though, is that we've put all the nastiness behind us, and we get along okay. My wife gets along okay with her. Hell, a girl I dated between wives gets along okay with both of them. So to hear that she's in Critical Care, her prognosis uncertain...

Uncertain. That means she might not make it, right? Yeah. That's what it means.

Not funny.

I need her to live. Public figures aside, I don't speak ill of the dead. I want her alive so I can continue to make ex-wife jokes. Dammit. The fact that she's a single mother with a 9 year old kid who would be orphaned has nothing whatsoever to do with it.

My grandfather died of pneumonia, long ago before I was born. His son, my uncle, did too - 15 years ago.

So please take my kvetching about having a cold as mere comic relief - I consider myself lucky.

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May 23, 2007 at 5:29pm

#510542

Buckets of Snot

I'm sick.

Also, I have a cold. It's been going on since Friday, and migrated from my throat to my chest, back into my throat, and up into my sinuses. I'm currently producing more fluid from my nose and lungs than I am taking in. Every time I drink a glass of water, or a can of Coke Zero, I go through an entire box of Kleenex.

Can someone please tell me why tissue boxes feature pictures of FLOWERS? I mean, I don't really care - allergies aren't my problem (I make up for it by producing rivers of snot every time I get a cold, which fortunately, isn't that often these days), but I'd imagine that people with allergies see the flowers and get triggered.

Of course, that could be a conspiracy on the part of Kleenex and Puffs to sell more tissues.

Periodically I have to clean the snot off my computer screen. No matter how careful I am, Old Faithful exceeds the capacity of the tissue to contain it.

Why am I putting in a blog entry guaranteed to gross everyone out? Well, because I don't believe in being miserable alone. Since I can't give y'all the cold, I'll have to settle for making you mildly nauseated.

Comment • View 4 comments

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