Complex Numbers (Book)

Blog Calendar

◄ December ► 2007
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

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

December 21, 2007 at 5:34pm

#556468

The Longest Night

Sat., Dec. 22, 2007, 1:08 A.M. EST (06:08 UT), marks the solstice—the beginning of winter in the Northern Hemisphere

http://www.infoplease.com/spot/wintersolstice1.html

For those of us situated to the north of the Earth's equator, tonight is the longest night of the year.

Where I am, the sun has already set and the Night has begun, and it will not end until 7:27 am tomorrow.

My life isn't particularly dark right now. It's a good life, and I wouldn't trade it for anything. Okay, I'd like my back pain to go away, but other than that I have no real complaints.

It hasn't always been like that. Like most people, I've had my ups and downs, and I fully expect I'll continue to have them. The ups are like summer: sunny, carefree, bright, cheerful. The downs? Well, there's a lot of fake "cheer" going around these days, usually bedecked in red and green with a price tag swinging from it in the snow-flecked breeze, but I don't find much cheerful about winter. I mean, in winter, through the longest nights, we have to make our own cheer, be it bright lights, dancing fires, the company of friends and lovers.

The ups and downs of the seasons are fairly predictable. Not so those of humans. I suppose many of us suffer from seasonal depression. Not me. I just get depressed at random times. Then I get, "What do you have to be depressed about? You have such a great life! Friends, family, people who care, and all the stuff you've ever wanted!" and so on. And so I feel guilty about feeling bad in the midst of all of that, which makes me feel even worse, which leads to more protestations on the part of well-meaning friends, which makes me want to go away from them, which makes things worse, until I, for no reason I can ever properly elucidate, feel like I'm living my own longest night.

See, people are always telling me to "count my blessings." It was one of my mother's favorite phrases. I never did fully understand it. "Count your blessings," she'd say. Like when you're lying awake at night and instead of fluffy white sheep hopping a fence, you see little blessings - whatever the fuck they look like - and you can fall right asleep. It's not that I can't count my blessings; it's not that I can't be thankful for all that I have.

It's that I'm scared shitless that I'll lose it all.

On the solstice, I have in the past had a personal tradition to remain awake all night in a kind of vigil, to force myself to endure Nature's longest night in hopes that it will, through some psychology or sympathetic magic, allow me to withstand my personal ones.

I don't know if I can do that tonight. I didn't sleep well last night, and I'm not sure I can stay awake. I'm not sure if I want to. I've done the vigil a few times, and I think I've gotten out of it what I need to.

The night is no darker than any other, really. In fact, tonight it should be even brighter than usual - it's almost a full moon, and even if it's cloudy, the clouds will shine from the reflected fake cheer hung from everyone's trees and houses. It's a bright enough night, but neither moon nor blinking red and green lights can hold a candle to the light of the Sun. As dawn approaches, the light intensifies, and its quality becomes crepuscular. I love that word - crepuscular - and I don't get to use it often enough. "Of or pertaining to twilight." For a while, the world hangs in the crepuscular balance between night and day and then - slowly, so slowly that you can no more detect it than you can detect the movement of the hour hand on an analog clock - the day begins.

Dawn doesn't break; it melts.

As it has done since before human history, the world wakes up from its long night as a sliver of sun peers over the horizon. In contrast to the steady melting of night into day, it takes a surprisingly short time for the solar disk to crest the horizon - at which point you're really not supposed to look at it anymore, but I figure the UV has been scattered away and I have just a few seconds to contemplate that which makes life possible here on this remote speck of a world, so small in the universe yet so large to us.

It's all a matter of perspective, isn't it?

Sunrise: one of the few things that we can say with certainty that it will happen tomorrow. Because it defines tomorrow.

It's not long before I have to look away. The light is only burned on my retinas for a few short moments, but it's burned into my memory forever: There will be a tomorrow, and things will cycle back to summer.

Mama always told me not to look into the sights of the sun.
Oh but Mama,
That's where the fun is.

Comment • View 5 comments

December 21, 2007 at 5:01pm

#556457

I must be a bad person...

...because this made me laugh.

http://www.canada.com/reginaleaderpost/news/story.html?id=4e53b7c3-1200-4748-ab8...

"I told Maya: 'There's a letter from Santa just for you, let's read it'. We sat down on the couch, I opened the letter and began to read. My mouth dropped open. Oh, My God!"

Speaking of bad people, this quiz might help you choose from amongst the plethora of evils visited upon us by the Republicrats and Democans vying for the Presidential election. Why they'd actually want the job is beyond me - it's like volunteering to clean up a Superfund site without a biohazard suit.

Anyway,

http://www.wqad.com/Global/link.asp?L=259460

Answer the 11 questions below to find out which candidates are most aligned with your views and opinions. You may skip questions if you do not want them factored into the results. This quiz is not meant to pick your candidate for you. It is designed to inform the public of the various stances candidates make.

I ended up with Rudy Giuliani. You know... the guy Pat Robertson endorsed?

I think I'd rather write in Hello Kitty

Speaking of disgusting things that are bad for you:

http://www.supersizedmeals.com/food/

Having a hard time deciding what to buy your friends or relatives this Christmas? Why not make them something instead! Everyone always says, "everything tastes better with bacon", why should chocolate be any different?

Comment • View 7 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.