Complex Numbers (Book)

Blog Calendar

◄ September ► 2008
S	M	T	W	T	F	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

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

September 21, 2008 at 4:40pm

#608528

Further Thoughts on Our Impending Doom

elusive ennui warm inside

: To quote Don Henley, "They ain't here; they ain't coming." I sometimes envy the truly religious - that is, anyone who believes there's an external entity, be it God, Odin, Barack Obama or Space Aliens, that will, if we pray or sacrifice or vote or wish hard enough, come to rescue ourselves from ourselves. I sometimes envy them because I don't think wishing's going to make it so. Oh, Obama might become President, sure, but he's still not going to save us from ourselves.

We have to do that, and we're doing a piss-poor job of it while all we do is watch TV, surf the Internet, complain about gas prices and blog.

Thomas

: The rise and fall, the changing fortunes, of business is the cornerstone of capitalism, and it is, simultaneously, its boon and its bane. But that cycle depends on the natural waxing and waning of peoples' needs and faddish desires. And sometimes, something very fundamental changes - imagine what would have happened had government bailed out carriage makers at the beginning of the last century, or typewriter manufacturers at the end of it.

I'm not saying that the need for banking is obsolete, but clearly some of the practices of bankers (that group for which British author Neil Gaiman said the collective noun for was a "wunch") were doomed to failure and, just as evolutionary pressures force some organisms to adapt or die, the evolutionary pressure of business should force some businesses to adapt or die - whether the business is making carriages that were destined to be replaced by motor vehicles, or repackaging bad loans into worse investment vehicles.

orangefiire: I'm talking about the economic problems here in the US, starting with the deflation of the housing price bubble and its ripple effect on banks, insurance companies, the Federal Reserve, and ultimately all of us in the US. And probably some foreigners as well, but no one cares about them unless we have a military force over there. Wherever "there" is.

Just kidding, AL

and Mavis Moog

The StoryMaster

: The broker (one which doesn't appear to be part of the collapse) that holds part of my portfolio had a portion of said portfolio in AIG; they only sold it recently, after it had tanked. Before that, they sold the portfolio's position in LEH - after it tanked. Back in 2001 or whenever it was, they also sold its position in Enron - after it tanked.

With the market the way it is, I may just have to wrest control back from the "professional investment advisers" and put it all into Apple and Netflix stock. I figure no matter what happens to the rest of the economy, people will still want their iPods and movies... cheap entertainment while we're all sitting at home, jobless.

Anyway, I do think you're right, SM, in that we as a country are still going to be in a good position to recover from this. And that it's not exactly business as usual. But if I got handed a severance package of $10M or more, I'd take the scrutiny... I could live pretty well for the rest of my life on $10M and to hell with the investigators. I'd like to see them FIND me in Belize. Oops, did I say where I was going? I meant Fiji. Yep, moving to Fiji; look for me there.

I do think banks will continue to lend money, just not as freely as they have in the past, and to me that's a GOOD thing - having an economy based on fake money created by debt is no way to run a country; as I recall, it was unregulated buying on margin that was a major trigger for the Great Depression (which, when all is said and done with the coming Depression, may be renamed as the Great Manic) in the first place, and while there's less *direct* buying on margin, it's apparent that a lot of the 'money' in the market over the past few years has been borrowed.

As for buying businesses at an utter steal... unless Warren Buffett buys it, it's probably not as good a deal as we think

: I'm not a socialist, and Sarah Palin scares me to death, too. Apparently mediocrity isn't just fashionable anymore; it's entrenched.

Give me an intellectual elitist ANY day of the week. But especially on Election Day.

Comment • View 9 comments

© Copyright 2025 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.