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 5, 2009 at 4:02pm

#634096

Adoption

4. I was adopted.

I've never made a secret of this, but it's not exactly something that comes up in casual conversation.

My parents never made a secret of it, either. One of my early memories involves me telling this to some shocked adult who had commented on my resemblance to my father.

Any physical resemblance to my father is coincidental. (What was that long-ago adult thinking, anyway? Dad had black hair and deep brown eyes and a huge Jewish honker. I had blond hair (since darkened) and blue eyes (which I still have) and a straight European nose.) Any other resemblance to my father is probably intentional on my part, and I take it as a compliment.

The first thing people usually ask me is, "Do you know who your biological parents are?" Which is a perfectly reasonable question. "Do you know who your real parents are?" gets an unequivocal "Yes," and nothing more. It's rude. Anyway, to answer the non-rude version, no, I don't. At least, not entirely. I've learned a name, which I discovered when I went through Dad's safe-deposit box after he was declared incompetent due to Alzheimer's. Actually, I learned two names, my biological mother's, and my birth name.

This latter surprised me. I mean, I always knew I had a biological mother and father, though I never knew or cared to know their names. But what I didn't know was that the person who birthed me had given me a name, before my adoptive parents gave me the name on my birth certificate.

The papers don't disclose my biological father's name, and to tell the truth, I haven't given him much thought. This was the mid-sixties in the midwest, and the sexual revolution was getting going. Even without that, it wasn't exactly unheard of for a woman in college to get knocked up and then give the kid away so as not to jeopardize her education or life. I suppose a few years later, when it was legal, it was more common for such women to get an abortion. I suppose I should be grateful for that, but really, if she'd gotten an abortion, I wouldn't be here to be ungrateful, so who cares? I'm completely pro-choice anyway.

I've known several people who were adopted, and there's nothing that we all have in common save that we were adopted. Some were abused; some were not. Some were pushed aside in favor of their parents' genetic offspring; others weren't. I can say that in my case, it made me know, for a fact, beyond a doubt, that my parents wanted me; some kids could think they were accidents, but never me.

It's just not something that matters, especially now that my parents are dead and, as best as I've been able to determine, my genetic mother died in '89. Could have been someone else with the same name who was in her late teens when I was born. I haven't looked deeper into it.

My birth name, discovered in my father's papers? Robert Waltz.

You don't think I'd use my real name on the internet, do you?

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