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

December 25, 2007 at 11:25am

#557036

Let's try this again.

I have this intense back pain that's coloring everything I say or do. And it doesn't help that this computer keeps crashing, usually whenever I do something like try to figure out WHY it's crashing. So I'm grumpy - grumpier than usual, anyway.

But it's Christmas.

And though Christmas has never been my holiday, I think that on Christmas - whichever Christmas you observe, be it the commemoration of Jesus' birth, a time to make kids happy, a time to run up debt and keep stores in business, a day to be with family, a day of peace and contemplation, or even just a day when you don't have to be at work, or whatever - you should be nice to people. It's the one day when you can get away with that without other people thinking you want something in return.

There's not much I like when it comes to Christmas songs. I prefer the parodies and the fringe songs to the jingle bells and silent nights. But there's one Christmas song that I always like to hear and, fortunately, the rock station I listen to at home plays it from time to time in December.

Greg Lake, of Emerson Lake and Palmer fame, did the song, called "I Believe in Father Christmas." And even though its message - deploring the commercialization of what he feels should be a spiritual holiday is not one that I totally agree with, I like it anyway. You have to hear the song to get the full effect, but the lyrics pretty much stand on their own.

They said there'll be snow at Christmas,
They said there'll be peace on earth,
But instead it just kept on raining,
A veil of tears for the Virgin birth.

I remember one Christmas morning,
The Winter's light and a distant choir,
And the peal of a bell and that Christmas tree smell,
And eyes full of tinsel and fire.

They sold me a dream of Christmas,
They sold me a silent night,
They told me a fairy story,
'Til I believed in the Israelite.

And I believed in Father Christmas,
And I looked to the sky with excited eyes,
Then I woke with a yawn in the first light of dawn,
And I saw him and through his disguise.

I wish you a hopeful Christmas,
I wish you a brave New Year,
All anguish, pain and sadness,
Leave your heart and let your road be clear.

They said there'd be snow at Christmas,
They said there'd be peace on earth,
Hallelujah! Noel!, be it Heaven or Hell,
The Christmas we get, we deserve.

Have a great one.

Comment • View 3 comments

December 25, 2007 at 10:23am

#557031

Gift Exchange

If you're not familiar with the idea, it goes something like this:

-Everybody brings a pressie, usually with a cost range involved
-Names are drawn one by one out of a hat.
-The first name drawn picks a wrapped pressie.
-The second name drawn decides whether to pick a wrapped pressie, or whisk the first person's pressie away, laughing hysterically.
-If your opened pressie is stolen, you can unwrap a new one.
-The third person likewise has a choice between a wrapped pressie or ANY of the previously opened pressies, whether they've been previously stolen or not.
-After the last person makes the choice, the first person gets one free pick from all the previously opened pressies.

Whoever thought of this "tradition" should be lowered inch by inch into concentrated hydrochloric acid. Whoever perpetrates this "tradition" onto anyone else should be shot. If the perpetratees are family, the person with the bright idea of perpetrating this "tradition" should be shot in the knees first.

That is all.

Comment • View 3 comments

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