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

November 9, 2007 at 5:20pm

#548068

B minus 2 Days

Bruce has long been concerned about social issues, and rather outspoken about them at concerts. But he never stated a particular political opinion until 2004.

Partly, this almost certainly had to do with trying not to alienate a segment of his fan base. You saw what happened to Dixie Chicks when they publicly said shit about Bush - though as relatively new country singers, they had more to lose than an established rock / folk performer.

But in 2004, Bruce had apparently had enough of the bullshit, and joined the Vote for Change initiative.

Naturally, I got tickets. I'd have gotten tickets even if I supported Bush, just to see Bruce on stage again. Oddly enough, Ticketmaster wouldn't let me get 2 tickets or 4 tickets - but it had no problem selling me 3 tickets. The show was in Philadelphia, because they were targeting "swing" states like Pennsylvania and Ohio, trying to push them toward the blue.

A lot of people felt betrayed by Bruce at that point, because as I said, never before had he come out in favor of one party or the other. How anyone could mistake him for a conservative, though, is beyond me - but hey, Reagan made that mistake in 1984.

The real problem, in my opinion, is that America doesn't really divide into merely liberals and conservatives, and those that think it does are a bigger problem than either liberals or conservatives. These people don't listen to actual debates anymore; they just check to see if the content of the speech is more in line with "liberal" or "conservative" values and either dismiss it if it's not the same as their own, or quote it like Truth if it is.

In other words, a closed-minded Springsteen fan would see that he is supporting the Democrats, and immediately stop being a fan. This doesn't make sense to me. It would be, like, say you appreciate a certain actor. Let's say Brad Pitt. One day it comes out that Brad Pitt is actually gay. So you stop liking Brad Pitt because he's gay. He's not any different as an actor - so what changed? Nothing but your perception.

Well, anyway, the important thing is: was it a good concert?

Hell, yeah.

Since we had a third ticket, we dragged ArtemisMad Scientist

along. In addition to Bruce, there was a warm-up performance by Bright Eyes - who I'd never heard of, but has become one of my favorite bands. Then it was Bruce and R.E.M. alternating songs, even sharing band members.

Let me tell you something: watching Bruce and Michael Stipe alternating verses on Man on the Moon was a peak experience for me. Awesome song. Awesome movie. Andy Kaufman was awesome, too. You know he's buried in the same cemetery as my mom? If he's really buried, that is...

Oh yeah, John Fogerty came out for a couple songs, too.

Obviously, the attempt to swing the vote wasn't successful; Bruce saw his shadow and we had four more years of winter. But the concert was spectacular.

The ragamuffin gunner is returnin' home like a hungry runaway
He walks through town all alone
He must be from the fort he hears the high school girls say
His countryside's burnin' with wolfman fairies dressed in drag for homicide
The hit and run, plead sanctuary, 'neath a holy stone they hide
They're breakin' beams and crosses with a spastic's reelin' perfection
nuns run bald through Vatican halls pregnant, pleadin' immaculate conception
And everybody's wrecked on Main Street from drinking unholy blood
Sticker smiles sweet as gunner breathes deep, his ankles caked in mud
And I said "Hey, gunner man, that's quicksand, that's quicksand that ain't mud
Have you thrown your senses to the war or did you lose them in the flood?"

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November 9, 2007 at 10:04am

#547950

Opportunity of a Lifetime

One of my homies dropped out of going to the Springsteen concert on Sunday. Her loss.

I hate to see a ticket go to waste (I have six total), and I don't have time to sell it - nor will I scalp it; I don't believe in that. So if YOU, dear Reader, can get to Washington, DC by around 6:30 pm on Sunday, you can join us. Not only will you get to see the greatest musician of all time, you'll get to meet ME! Oh, and ArtemisMad Scientist

, too.

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