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

Stik to My Own Beat

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 wanderlust-words-in-motion

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 wanderlust-words-in-motion

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 Surprised

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 13, 2012 at 7:10pm

#752803

Damn close.

How To Have A Damn Near Perfect Day, Waltz Edition:

1. Sleep late (imperative for the Damn Near Perfect Day, or even the Perfect one.)

2. Good company (my friend Artemismad

).

3. Brunch at a country diner.

4. Wine tastings all afternoon in the Blue Ridge area.

5. Dinner at a microbrewery with excellent food and better beer.

6. Dar

Williams concert in the evening.

I mean, really, it doesn't get much better than this. Springsteen would have to be involved for that. And probably sex. No, not at the same time, you filthy-minded perverts.

Man, tomorrow is going to suck.

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May 3, 2012 at 3:51pm

#752221

Some Assembly Required

Okay, I'm way-out-of-proportion pumped for the Avengers movie. Yes, I am a movie geek and a comic book geek, so this is like... one of the highlights of my life. As a proper geek, I already have my tickets and will be viewing the midnight show tonight.

In preparation for this blessed event, I've been neglecting my actual projects (work, writing, home maintenance, eating, showers) in favor of watching all the Avengers tie-in movies: Iron Man. Iron Man 2, Captain America, The Incredible Hulk, and Thor. (Silver is Back!

, I'll be writing more once I've seen Avengers. Pinky promise.)

So I was watching Hulk last night and I commented on it to my friend PuppyTales

, who proceeded to relate to me the Greatest Movie Synopsis Ever, which I don't feel right posting because it's not my work. I will if she gives me permission.

But it reminded me that the character of Emil Blonsky, the movie's biggest bad guy, was portrayed by Tim Roth, whose other notable role was a petty thief in Pulp Fiction.

In the Avengers tie-ins, one of the main characters is Nick Fury, portrayed by professional badass Samuel L. Jackson.

Fury does not appear in Hulk, though he's in the other tie-ins, and so I feel like Marvel missed out on a great opportunity here.

See, they could have had Fury and Blonsky meet in a diner, as he did with Tony Stark in IM2. Best, Fury has the Cosmic Cube with him. The Cosmic Cube is that thing in Captain America that the Red Skull opens a box and it glows in his face.

With me? Yes, they missed the opportunity to riff on the scene in Pulp Fiction between Jules and Ringo ("Pumpkin.")

I'd pay to see that.

I'd pay TRIPLE to see that.

And Marvel blew it.

There's a passage I got memorized. Ezekiel 25:17. "The path of the righteous man is beset on all sides by the inequities of the selfish and the tyranny of evil men. Blessed is he who, in the name of charity and good will, shepherds the weak through the valley of the darkness, for he is truly his brother's keeper and the finder of lost children. And I will strike down upon thee with great vengeance and furious anger those who attempt to poison and destroy My brothers. And you will know I am the Lord when I lay My vengeance upon you." Now... I been sayin' that shit for years. And if you ever heard it, that meant your ass. You'd be dead right now. I never gave much thought to what it meant. I just thought it was a cold-blooded thing to say to a motherfucker before I popped a cap in his ass. But I saw some shit this mornin' made me think twice. See, now I'm thinking: maybe it means you're the evil man. And I'm the righteous man. And Mr. 9mm here... he's the shepherd protecting my righteous ass in the valley of darkness. Or it could mean you're the righteous man and I'm the shepherd and it's the world that's evil and selfish. And I'd like that. But that shit ain't the truth. The truth is you're the weak. And I'm the tyranny of evil men. But I'm tryin', Blonsky. I'm tryin' real hard... to be the shepherd.

In researching this blog post, I discovered that Pulp Fiction came out 18 years ago. There are people who can vote this year in the Presidential election who were not alive when that movie was made.

I'm going to go crawl into a bottle now and imagine how things would be different if Tarantino had directed the Avengers universe movies.

Edited to add:

With permission, Puppy's movie synopsis:

"The Incredible Hulk.

In which Tyler Durden's alter ego has stolen Aragorn's elf girlfriend, and must fight Pumpkin."

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