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

January 7, 2008 at 6:33pm

#559579

Signs of the Coming Apocalypse

First in our Web of Wrong today, we have this heartworming story about a couple denied their child due to their religion - or, specifically and just as chilling, lack thereof:

http://www.time.com/time/magazine/article/0,9171,877155,00.html

Inestimable Privilege. In an extraordinary decision, Judge Camarata denied the Burkes' right to the child because of their lack of belief in a Supreme Being. Despite the Burkes' "high moral and ethical standards," he said, the New Jersey state constitution declares that "no person shall be deprived of the inestimable privilege of worshiping Almighty God in a manner agreeable to the dictates of his own conscience."

This is especially appalling to me because my own parents had to wait until they were 50 to have a child - because no agency would adopt out a child to non-Christian parents.

I hereby begin my list of Candidates for Douchenozzle of the Year with Judge Camarata.

But it might not matter, because clearly, the End is Nigh, and it might come with the U.S. Presidential Election:

http://www.physorg.com/news118756781.html

Former Arkansas governor Huckabee said in a debate in May that he did not believe in evolution.

A poll conducted last year showed that 53 percent of Americans do believe that humans developed over millions of years from less advanced forms of life -- the theory of evolution -- while 47 percent do not.

Forty Fucking Seven Percent? That's it. We're doomed. 47% of Americans can't understand or accept the scientific reasoning that we developed out of a different form of life, despite the crushing weight of overwhelming evidence? Look, I don't care if you believe your Invisible Friend guided evolution; there was still evolution. I also don't care that the scientists can't agree on the precise mechanisms that drive evolution; that's called scientific debate and it goes on all the time. Come to think of it, I don't care what you believe, period - until it starts to affect public policy. 47%? No wonder judges are being douchenozzles about religion.

But, lest you think that the proof of Ragnarok's approach is purely religious, I give you People With More Time On Their Hands Than They Know What To Do With - so they post pictures of (admittedly interesting) automobile accidents:

http://www.quazen.com/News/Alternative/10-Freak-Car-Accidents-2.71373

And speaking of automobile accidents, I bet they go UP - at least among male drivers - when these become standard equipment. I give you: the Porn-Inspired Airbag (link's pretty safe):

http://boinkology.com/2008/01/04/first-ever-porn-inspired-automobile-airbag/

But in case you were wondering exactly what form the eschaton will take, well, there are at least five possibilities - depending upon one's religion. Here's Cracked's list of the "most kick-ass" ones:

http://www.cracked.com/article_14977_5-most-kick-ass-apocalyptic-prophecies.html...

My personal favorite is #3:

What to watch for:
The arrival of white men in the lands of the Hopi Indians, taking land that isn't theirs and killing their enemies with hand-held thunder.

Wait a minute.

Uh oh.

But, speaking of Hopi, all Hope is not lost, as long as we have people doing this:

http://www.snotr.com/video/789

I mean... that's just plane COOL.

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