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

September 11, 2008 at 6:49pm

#606634

Constitutional

http://www.readthehook.com/stories/2008/09/11/COVER-amalg.aspx

Like a delicate butterfly emerging out of a bloated pink pupa, Montpelier has metamorphasized back into its original self, circa 1820. The change is dramatic, the stuccoed mansion expanded by William and Annie duPont is no more, and historians say that's a good thing.

Monticello gets all the attention around here. It's Mr. Jefferson's town, Mr. Jefferson's University, Mr. Jefferson's Hemp Farm, etc. Okay, sometimes Monroe gets a nod, because of Ash Lawn - Highland, which is near Monticello. And okay, I've been known to indulge in Jefferson-worship, myself.

James Madison, however, is a bit of an outcast in the rich-old-white-guy club, with his home closer to Orange (a tiny little town with three stoplights) than to Charlottesville. And like the article says, other people came along and fucked up his house beyond all recognition. I took tours of it back then - lots of art-deco crap, but a pretty neat garden. Mostly, though, I had to endure steeplechase runs on the vast Montpelier grounds - which would be fine, except for all the yuppies around.

There's probably a metaphor in there, somewhere - how the house of the dude who penned our Constitution has been modified, altered, added on to, and painted pink (PINK!) over the centuries, and now, finally, one guy with vision and persistence was able to restore it to its former condition. And how it sure would be nice if someone did something similar with the Constitution.

But the fact is that buildings crumble and have to be protected, and maintained; likewise, the Constitution can easily crumble and it, too, has to be protected and maintained. It's okay to add and subtract from it now and then - the amendment abolishing slavery, for example, was only wrong in that it never should have been necessary; likewise the amendment repealing Prohibition - but the essential form must remain the same, in spite of any efforts to hide it behind sprawling magnolias or pink stucco.

So let that be my nod to... what today is (other than Waltz Is Great Day, of course) - my hope that recent, shall we say, attempts to mask the Constitution, to make it look like other than what it is, can soon be carefully dismantled, so that something resembling its true self can be once more revealed. There's no excuse for what's happened. Not the passing fad of art deco, and not the bitter reek of fear.

The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized. - Amendment IV

Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted. - Amendment VIII

The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people. - Amendment IX

Yeah, there's probably a metaphor in there, somewhere, but I'm nowhere near subtle enough to tease it out.

I pretty much just hate the color pink.

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