Complex Numbers (Book)

Blog Calendar

◄ July ► 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

July 4, 2007 at 12:00pm

#519005

On this Fourth of July

Sandy, the fireworks are hailin' over Little Eden tonight
Forcin' the light into all those stoned-out faces left stranded on this Fourth of July
Down in town the circuit's full with switchblade lovers so fast so shiny so sharp
And the wizards play down on Pinball Way on the boardwalk way past dark
And the boys from the casino dance with their shirts open like Latin lovers along the shore
Chasin' all them silly New York girls

Sandy the aurora is risin' behind us
The pier lights our carnival life forever
Love me tonight for I may never see you again
Hey Sandy girl

The Fourth of July used to swell my heart with all the patriotic feelings that the advertisements demanded. My dad, who was a retired Coast Guard officer, wasn't one for oversentimental patriotism, but as a military officer, he showed the proper respect to our country and its heroes.

Then there were the fireworks.

I love fireworks. When I was a kid we'd buy those big honkin' packs of sparklers, spitters, spinners and snakes, and I'd spend all day on the Fourth sorting them into piles, deciding which ones to set off first, middle and last for the ultimate Fourth of July effect. "I'll start with the black snakes," I'd decide, "And then after the sun goes down we'll light some sparklers, and then get into the really fun stuff."

Now the greasers, they tramp the streets or get busted for trying to sleep on the beach all night
Them boys in their spiked high heels - ah, Sandy, their skins are so white
And me, I just got tired of hangin' in them dusty arcades bangin' them pleasure machines
Chasin' the factory girls underneath the boardwalk where they promised to unsnap their jeans
And you know that tilt-a-whirl down on the south beach drag
I got on it last night and my shirt got caught
And that Joey kept me spinnin' I didn't think I'd ever get off

Oh Sandy the aurora is risin' behind us
The pier lights our carnival life on the water
Runnin' down the beach at night with my boss's daughter
Well he ain't my boss no more Sandy

When I got old enough to drive, I was also tired of the lame-ass shit Virginia allows for personal fireworks, and we went up to the Washington Monument in DC to see the real show - about a forty-five minute drive; we'd park at the Pentagon, which is right across the river, and take the Metro in to around the Smithsonian. I'd spend the day gawking around the Air and Space museum, looking at the BIG rockets, and then head down to the National Phallus for the show.

This started about the time they got the Beach Boys to play down there. Free concert. Some estimates put the crowd at upwards of half a million people, with all the attendant fights, heat stroke, thefts, and illegal fireworks (DC has even more draconian regulations on individuals' fireworks than VA). With the luck of the young, I was fine.

James Watt, then the Secretary of the Interior, banned Beach Boys concerts, claiming they attracted "the wrong element." I adopted that as my slogan. "Hello, [mother of prospective girlfriend]. I'm the Wrong Element. Pleased to meet you."

Sandy, the angels have lost our desire for us
I spoke to 'em just last night and they said they won't set themselves on fire for us anymore
Every summer when the weather gets hot they ride that road down from heaven on their Harleys they come and they go
And you can see 'em dressed like stars in all the cheap little seashore bars parked making love with their babies out on the Kokomo
Well the cops finally busted Madame Marie for tellin' fortunes better than they do
This boardwalk life for me is through
You know you ought to quit this scene too

Sandy the aurora's rising behind us, the pier lights our carnival life forever
Oh love me tonight and I promise I'll love you forever

Except for 1986, that is, when they rededicated the Statue of Liberty. My friend Dave from Baltimore and I hopped up to New York, with Born in the USA cranked up hard all the way, with the sunroof open and the windows down because we didn't have air conditioning, but it didn't matter.

"Drivin' out of Baltimore County, me and Dave on the Fourth of July..."

We got off the turnpike at Exit 8 so we could make our holy pilgrimage to the Land of Bruce, Freehold and Asbury Park.

It was a pit.

In New York, we walked from 42nd Street all the way down to the Battery, where they had a dozen barges in the Hudson and the East River, all with the same, synchronized fireworks display. The renovated Statue of Liberty shone bright in the flickering light.

Then I grew up, and I lost track of Dave, and I got married, divorced and my engineering license. I got married again, and I forgot about fireworks and big cities. The World Trade Center, near the Statue of Liberty, collapsed in a cloud of smoke. And whenever someone mentioned patriotism I got sick at heart, because I love this country and the principles on which it was founded, but I've never been so embarrassed to be an American.

I can hear the conservative chorus now: "So why don't you leave?"

Because I can still say these things. Because I can still be a thorn in your side. Because as long as I'm here, I haven't given up trying.

And today we're going over to our friends' house, in the middle of rural Virginia, for a barbecue and maybe some fireworks. We're bringing tequila and triple sec and frozen lime concentrate, and we're going to celebrate the Fourth of July by pigging out and getting drunk on Mexican liquor. Hell, I might even bring some gin so I can give a nod to the Brits while I'm at it. "Hail to the Queen. Aren't you glad we divorced you?"

I'm afraid patriotic thoughts will be absent from the celebration.

quoted lyrics by Bruce Springsteen,
4th of July, Asbury Park (Sandy)

Comment • View 1 comment

© 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.