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

June 16, 2008 at 4:11pm

#591372

Having a Bad Day?

I don't know about the rest of y'all, but I'm having a real Monday. I've had to redo something I've been working on twice today. And a guy came in earlier with a bunch of ground shots he'd taken of a parking lot - elevations, that is. Survey data, only he's a contractor, not a surveyor. So I was wondering why some of the shots were off by over forty feet, until it hit me - he'd added where he should have subtracted.

And people wonder why shit gets built wrong.

Anyway, it turned out to be a bad case of Monday on the part of the contractor.

Still... anytime you're feeling like you're having the Monday from Hell (and I could make a case for Monday the 16th being far, far worse than Friday the 13th, by virtue of the fact that it's Monday), remember this chick, whose day started out bad, got worse, and ended up with her sitting in a closet drinking Corona.

I mean... it wasn't even real beer:

http://www.thenewstribune.com/news/youandme/story/389467.html

I decide the only way this day’s going to get any better is if I sit in the closet – which is the only room with light that doesn’t have a toilet in it – and get drunk.

So I drank the six-pack of Corona by myself in my closet, crying. With the squeezy lime juice, because I didn’t have the dishes or silverware yet to cut the lime with.

Sounds like what I'd do to cope. Except I would be drinking real beer, I wouldn't lament the lack of lime (because real beer doesn't need lime), and I wouldn't be crying. I'm just saying.

I suppose there's one way to have a worse Monday, but only if you live in certain parts of Iowa.

On a totally different subject, I bet you didn't know that D&D was actually invented by the Romans nearly 2000 years ago:

http://www.christies.com/Lotfinder/lot_details.aspx?intObjectID=4205385&title=rd...

A ROMAN GLASS GAMING DIE
Circa 2nd Century A.D.
Deep blue-green in color, the large twenty-sided die incised with a distinct symbol on each of its faces
2 1/16 in. (5.2 cm.) wide

...

Several polyhedra in various materials with similar symbols are known from the Roman period. Modern scholarship has not yet established the game for which these dice were used.

Probably not actually Dungeons and Dragons, now that I think of it. More like "Battlements and Barbarians."

"Okay, Lucius, make a Dexterity roll. Oops, that's a fumble - your sandals slip and you pour the boiling oil all over your feet. Roll again - oh, no, you've just impaled yourself on your drusus. Better roll up a new character."

"Fine, I'm going to be a Visigoth this time."

"A Visigoth? Damn, you've got a lot of Gaul."

(Players pelt GameMaster with dice for making a pun no one will get for at least 1000 years. One rolls into a corner, only to be found by a history professor 1900 years later.)

Well, it might have happened that way.

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