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

July 17, 2008 at 2:55pm

#597015

The Power of Rock & Roll

There can be no clearer evidence of the world-shattering power of rock & roll in general - and Bruce Springsteen in particular - than the following article.

Did the Boss help bring down the Berlin Wall?

BERLIN - When Bruce Springsteen spoke out against the Berlin Wall at the biggest concert in East German history in 1988, no one in the crowd of 160,000 had the faintest idea that the symbol of the Cold War would soon be history.

http://www.msnbc.msn.com/id/25696021/>1=43001

“Springsteen’s concert and speech certainly contributed in a larger sense to the events leading up to the fall of the Wall,” said Gerd Dietrich, a historian at Berlin’s Humboldt University.

Okay, giving credit where credit is due, I have to give Pink Floyd partial credit. Still:

Springsteen stopped halfway through the three-hour show for a short speech — in heavily accented German:

“I want to tell you I’m not here for or against any government,” Springsteen said, as he pointedly introduced his rendition of the Bob Dylan ballad “Chimes of Freedom.”

“I came to play rock ’n’ roll for you East Berliners in the hope that one day all the barriers will be torn down.”

Well, of course we can't point the finger of responsibility at any one person. Like any action in a Communist country, the fall of the Wall was a group effort. Still, sometimes these things take a catalyst, or at least a Last Straw.

I had a friend in the Army at the time stationed in Germany, and he was there when the Wall came down. Got me a piece of it, too. I haven't the slightest idea where it is now - most likely at some point, some well-meaning cohabitant thought it was trash. Women - you gotta watch 'em every second (hmm, that's not such a bad thing).

“People didn’t want to leave when it was over,” [Cherno Zobatey] said [of the concert]. “The police gave up after a while. I walked back across town for about two hours and everywhere everyone was happy and on a real high. But it didn’t feel like a revolution, just yet anyhow.”

I forget who said it, but I've heard that it's not poverty that causes revolutions - it's the knowledge of poverty.

Twenty years later, Bruce is still working for social justice. And East Berlin? It's history.

Thanks to Deelyte- Chillin'

for sending me the link!

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