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 6, 2008 at 8:48pm

#611427

Red State Blues

While I've tried to stay out of direct politicking in my blog, here, I'm sure most of you know I lean toward Obama in the presidential race. I was on the fence until McCain picked that champion of proud ignorance, Sarah Palin, to be his third wiferunning mate, but doing so put me squarely in Obama's camp.

Living as I do in Virginia (albeit in a particularly liberal-leaning town), my support would normally mean exactly nothing; this state hasn't gone for a Democrat since before I was born. But check out this poll:

http://www.surveyusa.com/client/PollReportEmail.aspx?g=00f2d8fb-6a3b-425d-9f27-2...

There is movement among men, where immediately after the GOP convention, McCain led by 10, and where today Obama leads by 11.

Yeah, we're flip-floppers like that.

There is movement among whites, where McCain's once 22-point lead is today reduced to single digits.

Are you saying we might be pro-McCain because he's one of Us?

There is movement among the well-to-do, where today for the first time Obama leads.

That's because both of them want our money, but Obama's more up-front about it.

There is movement among pro-choice voters, where Obama's lead has doubled since August.

Ummmmm... could it be because McCain is ANTI-CHOICE, maybe? (okay, I'm sure he's that way just so he could get the Republican nomination, but we're sure about she-who-may-become-President-gods-forbid.)

But here's the important thing:

In Central Virginia, home of the Confederate White House, the Museum of the Confederacy and Appomattox, Obama today leads by 8.

That's right. Some of us aren't fighting the War of Northern Aggression anymore. And some of us care less about the color of someone's skin and more about what's under that skin.

It's still a month before the election; polls can lie, anything can happen between now and then, and I'm still convinced there's voting fraud going on in every state that matters, including mine. But here in Virginia, we're already making history.

I think Jefferson would be proud.

(Edited to add:)

Our sacred house of dreams has been abused, looted, and left in a terrible state of disrepair. It needs care; it needs saving, it needs defending against those who would sell it down the river for power or a quick buck. It needs strong arms, hearts, and minds. It needs someone with Senator Obama's understanding, temperateness, deliberativeness, maturity, compassion, toughness, and faith, to help us rebuild our house once again. But most importantly, it needs us. You and me. To build that house with the generosity that is at the heart of the American spirit. A house that is truer and big enough to contain the hopes and dreams of all of our fellow citizens. That is where our future lies. We will rise or fall as a people by our ability to accomplish this task. Now I don't know about you, but I want that dream back, I want my America back, I want my country back.

So now is the time to stand with Barack Obama and Joe Biden, roll up our sleeves, and come on up for the rising.
-Bruce Springsteen
October 4, 2008

http://www.brucespringsteen.net/news/index.html

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