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 9, 2009 at 8:06pm

#653855

Mixed Bag

So sometimes the funniest things come from links. It's not like I'm getting paid for providing the public service of making y'all laugh.

Here's an article about genetically engineered mosquitoes. Mosquitoes that are engineered to be malaria carriers. Super malaria carriers. In an effort to STOP malaria.

http://www.askmen.com/money/money-news/31_the-upside-of-malaria.html

WASHINGTON (AP) -- Think your job's tedious? Try beheading 100 mosquitoes an hour.

Gently, no smushing allowed. Malaria parasites lurk in these mosquitoes' salivary glands, and a small company on the outskirts of the nation's capital needs them unharmed for a dramatic test -- attempting the first live vaccine to fight malaria.

Holy Shit, don't these people read science fiction? In what bizarro universe is it a good idea to genetically engineer malaria-carrying mosquitos?

There's only one solution: Stock up on tonic. And gin.

(Tonic water is supposed to protect against malaria, though the stuff sold on the shelves now probably doesn't have enough quinine to work properly. Still, you have to wonder about a drink that, in order to make it taste better, you have to add gin. Don't get me wrong; I love gin. But I'm almost alone in that.)

Now, here's the cool thing about the internet. Whatever question you have, someone somewhere has an answer to it. It's not always the right answer, and it helps to have a healthy dose of smarts and skepticism, but here's the answer to, "Gee, I wonder if it would be possible to drive from North America to South America?"

http://en.wikipedia.org/wiki/Darien_Gap

Basically: No. And not just because the part between the US and Brazil is infested with guerrillas, peach-sized spiders and tourists.

The Darién Gap is a large swath of undeveloped swampland and forest separating Panama (Central America) and Colombia (South America). It measures just over 160 km (99 mi) long and about 50 km (31 mi) wide. It is not possible to cross between South America and Central America by land without passing through the Darién Gap. Roadbuilding through this area is expensive, and the environmental toll is steep. Political consensus in favor of road construction has not emerged. There is no existing road connection through the Darién Gap connecting North/Central America with South America. It is therefore the missing link of the Pan-American Highway.

Back on the comedy, here's more proof that the customer is almost NEVER right.

http://notalwaysright.com/third-times-not-a-charm/2065

And finally, someone shows graphically what I've been thinking:

http://graphjam.com/2009/06/09/song-chart-memes-fear/

And really, 'nuff said.

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