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.

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 24, 2007 at 5:52pm

#551342

Another Saturday Night

...and I ain't got no ideas for next week's Comedy newsletter, so I'm using this entry to bounce ideas off an audience - you know, kind of like that old video game Pong where you had to bounce a little digital "ball" off a couple of paddles on the other side of the screen? You two are the couple of paddles.

I suppose I could do something holiday-related - but, as I've mentioned before, I don't find the holidays all that amusing. More like irritating. If I could find a way to alchemically transmute "irritating" to "funny," things might be different.

We watched A Christmas Story last night - we actually own a copy, since it's one of Kirstin's holiday tradition movies, and it's one of the few holiday-themed movies that I actually like. I like it because while it's nostalgic and family-oriented, it also has an edge. There are little things that I find ceaselessly amusing, like when the camera cuts straight from the younger brother about to use the bathroom to something resembling cabbage stew boiling on a stove, or the kid who gets his tongue stuck on a cold metal lamppost.

Well, I suppose it would kinda be my job as a sometime comedy writer to perform the abovementioned transmutation of irritating to funny. That's what we do, right? We take something sacred, or profane, or irritating, or annoying, or completely mundane, and turn it around so people find a way to laugh at it.

Thing is, I didn't start out to be funny - I started out to write science fiction.

A common trick in science fiction, one which goes all the way back to its roots in Mary Shelley's Frankenstein, is to write in the Alien Observer.

The Alien Observer probably has some literary name, it's so common. The basic idea is that you have a society like our own that is visited by a stranger. The stranger is rarely the main character in the story; more often, he, she or it (it could be a computer or literal space alien) serves as a conscience or foil for the protagonist. A prime example is Heinlein's Man from Mars in Stranger in a Strange Land, but I could come up with dozens of examples if I weren't basically lazy. The A.O.'s purpose in the story, besides to help move the plot along, is to point out absurdities inherent in the reader's own society, culture or modes of behavior. (There's also the reverse, where the main character is a human in an alien world so the alien world can be conveyed through the eyes of someone familiar.)

What this has in common with humor writing is that a lot of humor is all about pointing out the absurdities in society, or in human behavior. The humorist has to be the Alien Observer, finding things that the rest of us take too seriously, or for granted. This is, in fact, a sacred duty; the court jester has long enjoyed protected status - in exchange for being a virtual outcast in the society that spawned him or her.

Comedy is essentially an antisocial activity, and its practitioners are often marginalized. When's the last time you had a drink with a clown? And I don't mean that weird guy from Accounting, either.

I'm not saying I'm marginalized, of course. Sure, I marginalize myself in many ways - avoiding television, staying out of retail stores, pursuing math as a hobby and the like - but I'm aware that I'm not nearly funny enough to suffer the Clown Curse. I'm just procrastinating the writing of the newsletter.

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