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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🌝 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.

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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.

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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

May 16, 2008 at 11:23pm

#585511

Community

There is, I think, no relationship in the world quite like the relationship between a bartender and a drinker.

This evening, I met my friend Pat at a local pseudo-Mexican restaurant that boasts a bar with a spectacular tequila selection. I was early, so I sat at the bar.

This particular bar has a Tequila Club card - a green card (heh) with 20 different tequilas on it, ranging from well dreck up through the golden reposados and anejos that make life worth living. Every new tequila earns you a punch on the card; when you've gotten all 20 punches every tequila from then until eternity is $1 off.

Tonight, I had the bartender punch my #11 tequila, which turned out to be a smooth, ticklish reposado whose name escapes me but which I can easily determine on my next visit. I'm perfectly content to drink fine tequila straight, but I also like margaritas - on the rocks, salted rim. While I waited, I watched the bartender struggle with the creation of two frozen margaritas. They were, in my professional opinion, too sludgy to drink, and he knew it.

"The solution," I said (as the guy on the barstool, I claim the right to wax philosophical about all matters relating to alcohol), "is to outlaw frozen margaritas. They're an abomination."

The bartender, a tall guy who looked like he was trying to work his way through grad school - philosophy or English, I figured - looked at me and nodded, grinning a grim grin. "Now that," he said, "is an excellent idea."

It wasn't three minutes (by the clock on the TV, which was playing some basketball game or other) before the waitress came back with the abominations. "They said these were undrinkable."

Another server came to the rescue. "I'll make 'em," she offered. The philosophy major (or so I assume) breathed a sigh of relief.

"I mean," I went on, seeing as he was just watching at this point, "they're so cold you can't even appreciate the tequila."

"Well, they ordered Cuervo gold," he noted.

I nodded sagely. "In that case, frozen may be appropriate. But the ice just numbs the taste buds in general, and all you taste is ice."

The girl making the replacement margaritas - a much more liquid attempt than the philosopher's - asserted that this happens all the time, that they lose a lot of money by having to chuck bad frozen margaritas. "Outlaw 'em," I said. "If they want abominations, give 'em wine spritzers."

Everyone in earshot chuckled, and the bartender asked me if I wanted another real margarita.

I sighed, exaggerating my disappointment at my circumstances. "No, I'm meeting someone for dinner, thanks." But somehow, we got a table as soon as he showed up, and the service was prompt, and the food was excellent.

And damn, that was a good margarita.

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