Complex Numbers (Book)

Blog Calendar

◄ October ► 2010
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
31
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

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

October 24, 2010 at 11:03pm

#709278

Second Thoughts

Before I get into what I meant to talk about today, a bit of a clarification:

In 1948, an issue of Sky and Telescope provided a misinterpretation of the meaning of "blue moon" that persisted until 1999 - and, in fact, persists to this day. The article in that magazine (which was a printed thing that presaged web pages) gave the definition of a blue moon as the second full moon in a calendar month.

That, as I mentioned, turns out to be an error. It turns out that the older, and more correct, meaning for blue moon is the third full moon in a season (as in winter, spring, summer, or fall) that contains four full moons. (Though there are complications with regard to how exactly a season is determined.) This realigns the moon names with their seasonal expectations. By this rule, there will be a blue moon next month,

http://www.inconstantmoon.com/cyc_blue.htm

http://www.panic.com/blog/2009/12/on-calendars/

As a further aside, this is a great example of both how mistakes become quoted as if they were fact, as well as of how the definitions of things can be mutable. In the end, of course, we live in a much different world than the old Farmer's Almanac did, and the cycles of the moon mean little to us in our modern life, when many of us don't even bother to look for the moon, let alone care about its phase (two days past full as I write this), and almost nobody cares about the names of the moon anymore. Hell, even the seasons don't have the hold on us that they used to - not in a world where we can get winter squash in July and green onions in December.

Don't get me wrong; I like technology, especially the technology that put dudes on that very same Moon. I just can't help but feel that we've lost something along the way.

Anyway...

Shawna had the "let's just be friends" talk with Mike yesterday evening. Mike was like "okay." I'm only disappointed because it reduces the amount of vicarious drama in my life. Doesn't make me want to get cable, though. So I guess she was having second thoughts, even though she'd initiated almost all of their activities, including attending Sexy Zombie Jello Wrestling.

I got to thinking about it, and I wondered if she was expecting him to put up a fight, or get angry, or something. I get the impression some women think they need that to validate their own feelings, or whatever. I don't know... seems to me that if he'd tried to convince her otherwise, that would be saying, "you're just a girl and you don't know your own mind," which of course would set the women's movement back further than Sexy Zombie Jello Wresting did. Way I see it, though, if that's the case, he's saved himself a lot of relationship drama.

But what do I know? I'm clearly not qualified to render opinions on relationships. I was just like, "Does that mean we can still hang out with her and just talk?"

He didn't know. Sometimes "let's be friends" means "I just don't want to see you."

Someone needs to write a goddamn dictionary.

Ladies: we're not subtle. Just tell us straight out. It saves us both a lot of hassle, that way. Most of us aren't stalkers, and if you don't want us, we'll pursue one of the three billion other women out there.

I'm having second thoughts, too. I've been working toward putting together Part 2 of Prototype, my NaNovel from two years ago. I figured Part 2 would be this year's NaNo. I've gone through the motions of the wonderful "October Novel Prep Challenge"

by Brandiwyn🎶Prep starts 10/1!

but the characters just aren't speaking to me, this time. I know where I want to take it, but I'm no longer thinking that NaNoWriMo is the appropriate venue for completing Prototype. It's just not going well for me.

There's another idea I've had bouncing around for a few years now, not science fiction but more urban fantasy, which had the working title of Avatars until fucking James Cameron released that goddamn smurf movie, thus ruining the title forever (even though my idea is completely different, and uses the old definition of "avatar.")

I think I'll have time to outline it and get ready to do the actual writing this year - all I have so far are vague ideas about the beginning, some scenes in the middle, the end, the two main characters, and the antagonists. Come to think of it, that's really all I need to start writing, but I'd prefer to go ahead and outline it first.

But it feels like giving up, even though I fully intend to edit and flesh out Prototype at some point... though we all know what my intentions are worth.

I don't know. I feel like I have to decide soon. Like, tomorrow.

Comment • View 4 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.