Complex Numbers (Book)

Blog Calendar

◄ September ► 2021
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:

Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

September 24, 2021 at 8:32am

#1017962

Hard, Erect Deck

Cats don't like change.

Oh, I'm sure there are exceptions, as there always are to such blanket statements. But my cats aren't one of those exceptions.

Ever since I've had this house, 25 years now, there's been a deck over a patio in the back (on the north side). While it's been patched every now and then, it's been basically the same deck. It was never waterproof; any rain or melting snow would just drip down onto the patio which, it being on the north side, rarely got any sunlight and hence stayed damp for a very long time as well as making it utterly useless in actual rain. The deck itself, being higher up, does get some sun, especially around the summer solstice when the accursed daystar is not far from overhead. During the shit season, winter, the house itself shades the deck.

Still, having a table set up with a big umbrella makes the deck, if not the patio beneath, useful to me in a wide range of weather conditions; it's only when the wind and/or rain is too strong that I'm forced to stay inside. And as much as I like to complain about the not-so-great outdoors, I do enjoy being on the deck (it's only a couple of steps to the refrigerator where the beer is). My cats, and those to whom my housemate belongs, have made great use of the deck as well. Some of them like to leap up onto it from a nearby fencepost rather than doing the difficult work of walking all the way around to the steps. Mostly, the cats like to find sunbeams to sit in, or shade if it's July. Also, they're quite fond of hopping up and sitting on the kitchen windowsill, outside, when they wish to inform me that it's time to bring them inside to give me the privilege of serving them a meal.

Ever since I got the house, though, I've wanted to get the deck rebuilt with a drainage system to keep most of the direct rain off the patio. No one seemed to understand what I wanted there, and I can't be arsed to build the damn thing myself, so I let it slide for many years. A couple of years ago, I started looking again in earnest. Got a few quotes, almost had another heart attack.

Finally, last year, my neighbor recommended a guy whom he'd hired several times, so I got a quote from that contractor that seemed reasonable. But they wouldn't be able to get to it for another year. Okay, fine, it's waited this long. The deck probably wouldn't collapse in the next year. Probably. Maybe. Hey, structural engineering wasn't my best subject, okay? I put down a deposit and signed the contract.

Then the contractor sent me a message over the summer: "Yeah, lumber prices have blown up. I can either refund your deposit or we can agree on a higher price."

Normally, a contractor pulls crap like that on me, I assume they're scamming and drop 'em. But as you probably know, lumber prices did indeed jump into the stratosphere over the summer, and besides, no one else seemed willing to tackle the job, so I agreed.

Monday I get an email: "We're starting tomorrow."

Great notice there. Still, not going to delay this any more, so fine.

Tuesday, they tore out the old deck.

The cats' brains went fizzle. As far as they were concerned, the world was ending. Some of them sat at the kitchen door that would now open onto a 12 foot drop, attempting to get me to make the deck magically reappear. They have the same reaction when it rains. They want very, very badly to go out on the deck, and then when I graciously obey their command by opening the door, they see disgusting water falling from the sky, and they look at me with that air of having been betrayed. How dare I make it wet? Don't I know that water is Cat Kryptonite? And don't get me started on snow. I have so many pictures of a single paw print in a dusting of snow on the deck. A single print, because they'd stick one little foot into it, go "Nope," and huff off back inside with a twitching tail, and then take the next hour to lick the offending substance off their tender paw pads.

Thing is, though, I understand their reaction to the construction. I'm not a big fan of changes in my environment, either. I mean, sure, sometimes I purposely get away and go somewhere else, but that's not the same thing; I know I'll be coming back to pretty much the same house and neighborhood. Like I said, I've lived here for a quarter-century, nearly twice as long as I lived in the place I always called "home," where I grew upspent my childhood between the ages of 4 and 17. And since 1996, apart from a couple of repairs, the deck and patio have always been there.

I know the replacement will be better. I have wanted this for a very long time. It's not even going to be that different, in terms of size: about 12x24 (that's in feet; for those who use a more rational system of measurement, call it 4x8). There will be lights. It will be sturdier, not feeling like it's going to collapse if I step too hard. And of course, the drainage will allow better use of the patio below. And yet I felt a sense of loss; something that has been a vital and everyday part of my existence just suddenly wasn't there anymore. So I, too, was unsettled, even though, unlike my feline overlords, I have a pretty good idea what to expect from the construction.

Wednesday it rained almost all day, so they didn't do any work.

Yesterday, Thursday, they got the supports up and the deck framed, complete with joists. After they'd gone for the day, I glanced out the kitchen window and behold, there was my void cat, Robin, sitting on the sill outside looking distressed. Seeing the deck seem to reappear, she'd made her usual leap from the fencepost and then further up to the sill. There was only one problem: the actual deck boards hadn't been set, and there's about 18" (do your own centimeter conversion) of yawning emptiness between joists, so she had no way to hop down when I opened the door to let her in. Nor would she be able to retrace her steps. And contrary to popular belief, cats can get seriously injured dropping from a second-floor ledge onto patio flagstones.

I had to step outside, balancing on the joists, and pick up the very reluctant cat with both hands. All four sets of claws had activated, so I also had to keep those murder needles away from me, stepping from joist to joist whilst holding a squirming, frightened feline at arm's length, until I could deposit her onto the kitchen floor. Whereupon she retracted the claws, shook herself, and flounced off like, "That wasn't so bad."

"But Waltz, why didn't you just open the kitchen window to let her in?" Because the cats have been known to react badly to that while on the sill, and I didn't want her slipping off while I did that.

Anyway, I know this is long -- and late; if you didn't see my notebook post from yesterday, I was indulging in some evening ethanotherapy -- so I'll stop here. Right now they're hammering away outside, and it is So. Damn. Loud.

5 Like • Comment • View 4 comments

© Copyright 2024 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.