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

March 13, 2012 at 10:08pm

#748887

Epiphany

I came to a sudden realization of Ultimate Truth the other day.

Here's the background: I heard that Guinness World Records was going to vastly reduce the scope of its print edition, relying more on its online edition. While I can't find any confirmation of that, it doesn't really matter for the purposes of my point here. (Encyclopaedia Britannica, by the way, is totally doing that - eliminating its tree-murdering edition entirely so it can focus on its website and on fending off the attacks of its main competitor, Wikipedia).

I vaguely remembered being presented with a copy of what was then known as the Guinness Book of World Records as a kid, so I went on Wikipedia to get some background on the famous reference book (Britannica is a paysite, you see).

There, I discovered that (according to Wikipedia, anyway), GBWR, now known simply as Guinness World Records, got its start in the 1950s when some dude from the Guinness brewery in Ireland needed to settle a drunken pub argument about which bird was faster. No, it wasn't about African vs. European swallows. Realizing that people needed something to settle drunken bar arguments, he conceived of a book that would list superlatives in hundreds of categories: tallest, heaviest, shortest, fastest, most, whatever.

I guess if you couldn't find the answer to your drunken pub argument in GBWR, you could always hit your opponent over the head with a copy, thus settling the argument once and for all. This option is not available with the online edition, unless you want to pay $400 for a new iPad.

Anyway, over the years, it became disassociated from the actual Guinness brewery, though it retained the name. And while early versions had categories like "most beer consumed in an hour," such categories were expurgated from later versions, because the publisher might get sued when someone died of alcohol poisoning while trying to break that record.

So, to sum up, a book that had its origins in a drunken pub argument (including someone who worked at a brewery) can, for legal reasons, no longer contain a "drinking" category.

Resulting epiphany: Life is cocked-up on a very fundamental level.

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