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 2, 2007 at 8:26pm

#518639

Theory of Suck

Okay, I was so caught up in the whirlpool of potential suck that was the last entry that I forgot the most important part.

Go back and read my last entry and the attached link if you have not done so already.

Ready?

Okay.

A guy I know has this theory. The theory is that Britney Spears, Lindsay Lohan, Paris Hilton, and a select few other "celebrities" are actually government agents.

That's right - they're agents of the federal government, and their job?

Official Distractions.

Yep. They're Official Distractions so that whenever the government is trying to keep our minds off something, like say a particularly nasty blunder like, oh, the war in Iraq or Bush's commuting of Libby's sentence

, they tell one of them to go do something outrageously stupid, immoral, indecent, or just plain rude. The press is on them like flies, and meanwhile no one notices that we're about to, say, nuke Iran or invade Canada.

Yep.

Official Distractions. That's the best any of us can come up with. I mean, no one can be that idiotic all on their own...

...can they?

Comment • View 5 comments

July 2, 2007 at 8:01pm

#518635

The Suck

Please, please, for the love of everything that is holy and pure in this world, let this be a hoax:

http://www.nzherald.co.nz/section/1501119/story.cfm?c_id=1501119&objectid=104486...

Because if it is not a hoax, then there is not only no God, but no justice or mercy in this poor world.

Lindsay Lohan has been tipped to play Paris Hilton in a movie of her life.

And as if that weren't bad enough,

...with Britney Spears singing the soundtrack.

Scientists at Fermilab should pay attention - there will be so much suck there that it might just recreate the conditions at the Big Bang, rendering unnecessary any further experiments into superconducting supercolliders.

At the very least, the high concentration of suck would implode, causing a time warp that would send itself back into time, ending the Permian era and beginning the triASSic.

Church attendance would decline as people realized, en masse, that there is no God.

It is the Triple Crown of suck.

Please, please tell me this is false, because if it is not there is only one good thing that can come of this: no matter how bad any other movie, book, play, painting, or whatever is, we can all say with one voice, "At least it doesn't suck as bad as that Paris Hilton movie."

Comment • View 3 comments

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