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

January 1, 2007 at 1:08pm

#478293

In with the New

Our New Year's Eve tradition has become going out for teppan yaki. The place is always packed that evening - even moreso last night than on previous New Year's Eves - but not so much that you can't move or hear yourself think.

There was a moment of panic when the table behind us installed a sprog in a high chair - it was getting close to 9:00, and babies out in crowded adult restaurants at that time are either asleep (good) or screamingly overtired (bad). Boding well for the new year, this was one of the former.

Its presumed parents then proceeded to order a drink the size of my head. The size of my head AFTER I get a couple of compliments. Apparently, it was one of their birthdays - not the kid, one of the parents'. But once I gaped at the drink, we were able to ignore that table and concentrate on the Japanese guy doing fun things with fire and food in front of us.

I indulged also, of course, but it was only two carafes of sake. Well, two and a half, maybe. The champagne - er, sham champagne, since I'm too cheap to get the real stuff from France - would come later.

Last year, the fortune cookie I received was... interesting. It kind of set the tone for my whole year. So I took my time peeling and cracking open this year's cookie, all the while keenly aware that "Misfortune Cookies"

[18+] was likely to affect my fortune-cookie karma. Of course, the people with me had to keep reminding me of that little item. "So what were some of the Misfortune Cookies?" my wife asked, forcing me to remember (and make up) some off the top of my head.

But when I looked at my slip of paper, while others were laughingly reading theirs with the obligatory "...in bed!" addendum, I smiled quietly and put it into my pocket.

Understand, I hold no more stock in fortune cookie fortunes than I do magic 8-balls. They're just fun, and often cleverly written, a sort of culinary haiku without the syllabic constraint. Still, this was a good one, especially considering some of the entries in my previous blog, so I kept it to myself.

After dinner, none of us had the energy to go out and face crowds. Well, most of us didn't. Those of us who are old. <cough, cough, lean> We went to Meghan's house, ate chocolate, drank champagne brut and watched Pulp Fiction. There was actually a guy in our group who had never seen the whole thing

just scenes here and there.

Midnight came during the scene where Butch and Marcellus are tied up, broken and bleeding, with ball gags in their mouths. So we paused it there and toasted. "To a great year! (and may we never end up like Butch and Marcellus!)"

This morning, I woke early with a mild headache (I'd forgotten to balance the sham-pain with enough water) that went away after a while. I went through my old blog, and found a way to preserve most of the comments - a laborious copy-paste operation into static items. It took three static items. Not sure why I did it - ego boost, or a desire to keep the words of wisdom some of you were kind enough to put there - but I hope to eventually edit them around to something comprehensible.

So... here we are. I've already gotten complaints about this blog's description, but I'm keeping it anyway - it suits what I'm trying to do here.

Also, while "The Waltz of Life"

was XGC, I rarely took advantage of the content rating - so I'm going to try an 18+ here. I'm sure my fellow mods will let me know if that turns out to be insufficient.

Well, I've written enough. I still have 1600 words to write in "Overcoming Adversity"

[XGC], so I'm going to take a break now.

Oh, the fortune cookie?

There is only one happiness in life: to love and be loved.

C·==‡==============>·
the pun is mightier than the sword

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