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 20, 2007 at 5:13pm

#489372

Let there be LIGHT!

So I ran across this interesting little tidbit:

http://www.businessweek.com/ap/financialnews/D8NDHKEG0.htm

The Australian government on Tuesday announced plans to phase out incandescent light bulbs and replace them with more energy-efficient compact fluorescent bulbs across the country...

In incandescent light bulbs, perfected for mass use by Thomas A. Edison in the late 19th century, electricity flows through a filament to create light. Much of the energy, however, is wasted in the form of heat.

Australia is not the only place looking to replace them with fluorescent lighting, which is more efficient and longer lasting.

In incandescent light bulbs, perfected for mass use by Thomas A. Edison in the late 19th century, electricity flows through a filament to create light. Much of the energy, however, is wasted in the form of heat.

Note how Edison is mentioned by name as the "perfector" of incandescent light bulbs. Note also how the inventor (or perfector) of flourescent lights isn't even mentioned in passing in the story.

This isn't new. The two of them had a battle about electric current transmission, too. Edison was sure DC power was the answer. So what if there was no way, at the time, to send DC more than a few blocks without significant losses from resistance? It was the way things would be because, by damn, Edison said so! Meanwhile, the other guy found a way to send power over far vaster distances: AC transmission, enabling the power source to be significantly removed from the user. Hence, a power plant at Niagara Falls was able to supply power to New York City.

There's a statue of him on Goat Island, between Niagara's Falls. Goat Island is ephemeral; erosion will eventually push the falls upstream and make the island, and presumably the statue, disappear.

Same guy invented radio. Marconi got the popular credit, but the patent went to Nikola Tesla.

It's said that Tesla refused a Nobel prize when he found that he'd have to share it with Edison.

And now, if the trend is indeed to phase out (pun intended) incandescent bulbs in favor of flourescents... well, to me it represents the final triumph of Tesla over his blustering rival, Edison. Let there be light - cheap, clean, efficient light!

Now if they can only make them a bit less industrial-looking...

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