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

October 20, 2008 at 8:00pm

#613895

Harvest

Time to harvest some blog fodder.

Ladies, skip this link. It's for guys.

http://www.mrsexist.com/

Of course, those shirts aren't funny at all.

I don't know which is more pathetic: an environmentalist trying to be funny:

http://www.treehugger.com/files/2008/02/leed_introduces.php

... or the comment, Criticism is welcome, but what is the point of the article??? proving that no, certain environmentalists don't have a sense of humor.

Bonus: pics of cute baby seals and cats.

Speaking of cute animals,

The 6 Cutest Animals That Can Still Destroy You

If animals could talk, they would spend most of their time calling us dicks and telling us to get off their land. The traits we think of as "cute" are often simply tricks animals have developed to get tourists to throw them food.

http://www.cracked.com/article_15853_6-cutest-animals-that-can-still-destroy-you...

The platypus is mother nature's way of saying, "I made this thing out of spare parts I found on the workshop floor, and it can still fucking cripple you."

Speaking of things that can kill you,

http://wcbstv.com/slideshows/what.a.way.20.290025.html?rid=1

Example:
2 of 39 :
In 2007, a cab driver found the naked bodies of a young man and young woman at the base of a 50-foot building in Columbia, S.C. Later, authorities found their clothing on the roof, leading them to believe the couple fell to their deaths while having sex.

With accompanying pix - sadly, the pic accompanying the above example is a map of South Carolina, pinpointing Columbia so everyone knows where the Dumbass Capital of the World is.

Last one for today, the opening shot in the war on "The War On..."

(warning: the following link contains an abstract drawing of *gasp* a NAKED BREAST. If that sort of thing won't play with the people monitoring your Internet use, don't click it.)

http://www.ruthlessreviews.com/reviews.cfm/id/1452/page/the_beast__the_war_on_th...

In the latter half of the 20th century, Americans were called to meet abstractions with metaphors in a series of gaudy figurations popularly called “The War On . . .” Intended to be wholly symbolic, rhetorical frameworks that loosely invoked the legendary national unity that accompanied America’s good wars, whichever those were, our Wars On various and sundry Things that Are Bad proved the power of language to mold behavior, for often the martial tone spilled into martial practice, and so we find heavily armed SWAT units kicking down doors like soldiers in Baghdad...

War is peace; freedom is slavery.

Revolution, bitches:
http://www.sinfest.net/archive_page.php?comicID=2966

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