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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Show Recent Comments

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

January 27, 2011 at 12:48pm

#716613

Sad News

Just received word that my aunt died this morning.

Not really unexpected - she was close to 90 and just basically died of old age.

But she was someone I was close to all my life, my mom's sister, who took me to Europe and Israel when I was eight, taught me how to use a computer shortly thereafter, and gave me my first summer internship... sort of.

She was a businesswoman in a world where women were supposed to be housewives or secretaries; a childfree single woman in a world where women were expected to have kids, not jobs, for fulfillment; an educator and a strong role model for both men and women. A feminist before feminism was cool.

She was a true New Yorker, having lived in the city all her life. Yet, she had the good fortune to travel around the world. She was witty, vibrant, and never took shit from anyone without giving it back tenfold.

She ran her own business school for many years, which I'm sure improved the lives of many people. The world is truly a little bit better for her having been in it.

So, soon, I'll be heading up to New York, where she'll be buried out on Long Island, not too far from her longtime home in Queens.

So long, Aunt Adele. Of all the people in the world that I miss, you're at the top of the list.

Comment • View 7 comments

January 22, 2011 at 1:23am

#716135

It Really Works

Most of us will never hit it big in music (unless your name is Michelle), but now we can come pretty close:

Generate your own album cover.

http://blog.mflow.com/make-your-bands-album-cover-how-t/

Some of the results are uncannily authentic.

Like this one:

http://flo.mu/gv7NQ2

And this one:

http://flo.mu/h2vWUB

And especially this one:

http://flo.mu/hlfyCx

Seriously. I could see them in stores. If, you know, there were still stores that sold albums. Or even CDs.

Comment • View 4 comments

January 2, 2011 at 10:27pm

#714593

More Proof...

...of how awesome I am.

I feed one cat outside and the other one inside, else the first cat, Ghost, would eat all of Kali's food after he was done with his. Kali's a slow eater.

I always put Ghost's food in the same place: on the deck, between the recycling bin and the cinderblock. (I keep a cinderblock on the deck in case I have something out there I need to keep from blowing away, or keep the raccoons out of... oh, hell, no, I have no idea where it came from and no good way to dispose of it so it sits there.)

So today I dumped Ghost's food into his plate, and, as usual, he comes running out of nowhere once he hears the can open. I think it's a genetic thing with cats; they're hard-wired to appear when a can opens.

I dump the food in his plate, and he runs around the deck looking for it.

"Ghost. It's over here."

"Where?"

"Here. HERE. Where it always is."

"Where?"

So I pick him up and put him at the plate, and he starts scarfing the disgusting cat food.

I come back in, where my roommate has heard the entire exchange, and I say:

"Not the sharpest claw on the scratching post, that one."

He looks at me.

"You're just way too proud of yourself for saying that."

"Even more proud that I just made it up."

That's how awesome I am.

Comment • View 4 comments

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