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

February 6, 2009 at 4:00pm

#634297

Fear Itself

http://www.time.com/time/arts/article/0,8599,1877187,00.html

Facebook's "25 Things About Me" meme seems harmless enough; people write 25 facts about themselves and post them on their Facebook pages, just as they do with videos, status updates and photos of last weekend's party. An estimated 5 million of these notes — that's 125 million facts — have appeared on the website within the past week. Assuming it takes someone 10 minutes to come up with their list, this recent bout of viral narcissism has sent roughly 800,000 hours of worktime productivity down the drain...

Piss off, bitch.

5. I fear success more than I fear failure.

Not really sure how to expand on this, but I'm on too much of a roll to stop now, even with sandy-vagina Time writers throwing a wet blanket over the very idea.

Which leads me to wonder how someone like that gets a job writing for Time. Maybe she's a free-lancer; maybe she's a full-Time writer (or would that be full-Time Warner?) (heh). It's not because she's saying anything fresh or funny. In her own words, "Most people aren't funny, they aren't insightful, and they share way too much." Pot, meet kettle.

In my own humble opinion, while I am not funny (looks, as they say, aren't everything), I do say - or write - funny things sometimes. Sometimes I can even be insightful. And yeah, I probably share way too much, but this here's MY blog, and in the immortal words of Eddie Murphy's father, "if you don' like it, you can get tha FUCK out" and "Your wife's a bigfoot, isn't she, Gus?"

Hint to Ms. Suddath: being random is not the same thing as being funny. Anyone with a computer can be random. Being funny involves, among other things, taking two random things and finding a connection between them in some way that, in retrospect, makes a weird kind of sense.

To take random examples from the list she compiles in the above-referenced article,

9. I can't grow hair on my arms.

and

16. A horse once fell over while I was riding it.

I'd say, "What do you expect? It thought your completely furless arms were snakes and freaked out."

Maybe that's not roll-on-the-floor hilarious, but I smiled when I thought of it.

Which brings me back to why I fear success. Ms. Suddath is successful enough to have been published by a major publisher, Time magazine. I, on the other hand, have been published by, well, me. Here. And that's all. So who the hell am I to criticize a paid, published writer?

And when I'm published, what kind of idiot bloggers who can't be published to save their lives are going to be talking shit about me?

See why I fear success, now?

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