Complex Numbers (Book)

Blog Calendar

◄ September ► 2020
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:

Write_Mikey_Write!

about 3 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 5 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

September 10, 2020 at 12:26am

#992939

The Sound of Silence

There's an old riddle: Name me and so you will break me.

PROMPT September 10th

In your entry today, write about silence. Consider silence in both your personal life and in your writing. What messages can be conveyed through silence? Is there power in a person being silent? When is it appropriate to be silent and when is it not?

Yeah, yeah, I know - the Disturbed version is awesome. But Brandi

Carlile will always be my favorite, even if that particular song only features her backup singers.

Yesterday, I tried to drive my car for the first time in six months. It's been sitting on the street directly in front of my house, unmoving, silent. You know what I wish wasn't silent? When, sometime in the last six months, some asshole broke into it, opened the glovebox, and thus turned on a light that drained my battery. Might have been nice to actually have a working car alarm, then; I was probably in my house and I would have heard it. Instead, it was silent.

No need for shock or sympathy, there -- for some unknown reason, they broke in but didn't steal anything. My GPS is still there. The petty change that litters pretty much every central console of every car in the universe is still there. My personal Breathalyzer is still there, as is my mascot, a plush Dogmeat from Fallout 4. Hell, the big honkin' knife I keep in the back for emergencies is still there, and that sucker wasn't cheap. Even everything that had been in the glovebox - mostly the manual and some CDs -- was relocated but not stolen. It's more puzzling than anything else. I mean, if you're going to break into someone's car, fucking at least steal something. I mean, okay, it's possible something is missing; I don't exactly keep a pristine car interior. But if so, it's nothing I'll miss.

So I'm out $150 for a new battery, but big deal. If I'd gone on driving as usual, I'd have spent more than that in gas and maintenance.

Only thing I can figure is maybe they were specifically looking for a handgun. This is America, after all. Never kept one in the car, though.

Segué to the most obvious carriers of handguns: cops. I always wondered if I'd stick to my guns (pun intended) if I was ever arrested (I haven't been). I always imagined the cop would read me my Miranda rights like they do on TV. "You have the right to remain silent." At which point I'd clam up and say not even one word until I, somehow, hooked up with an attorney. The exact method of contacting an attorney when one isn't speaking a single word has always been a mystery to me.

Knowing me, I'd fail. But that's one time when silence is absolutely appropriate: when one is arrested and "anything you say can and will be used against you."

But silence can speak volumes. Fifth Amendment aside, spouses, for example, can and do use your silence against you. Her: "Do you think she's prettier than I am?" Me: *clams up while deciding whether to lie or tell the truth* Her: "I KNEW IT!" And then five or six days of the silent treatment.

There's an old, well-known Zen koan: if a tree falls in the forest and there's no one around to hear it, does it make a sound? Well, a sound is the vibration of air molecules; an ear isn't required. So... yes.

And yes, I'm well aware of the related joke: If a man speaks in the forest and there's no woman around to hear him, is he still wrong?

These days, silence is vastly underrated. I've mentioned before that I despise television with its blaring, constant noises. Here on the internet, though, there's never silence: everyone has a voice and seems determined to use it (metaphorically, at least; it's no accident that the second-most-popular social medium is called Twitter). And there's a lot of chatter about refusing to "be silenced."

This makes sense, though. It's one thing to choose silence for oneself. It's quite another to have it imposed upon one.

Which reminds me of an old joke.

A monk joins an order that requires a vow of silence. Upon joining, he's told he can speak only two words every five years. So, after being there for five years, he gets summoned to the head monk's office. "You may speak two words now." So he says, "Bed hard." They promise to switch out his mattress for a softer one. Five years later, he's summoned again. "Food cold," he says. I don't remember if they do anything about that or not; it's irrelevant. After another five years, he gets summoned a third time, and this time says, "I quit."

"I'm not surprised," says the head monk. "Since you got here, all you've done is complain."

Still. Not every silence is uncomfortable. I often wish we'd learn to live with the stillness and not fill it with meaningless twitter.

Today is my dad's birthday, and he is now forever silent. As will be the fate of us all. We should learn to get used to it.

The answer to the riddle way up at the top, if you haven't figured it out, is of course "silence." It's like a hole, I think: not an object in and of itself, but defined by what's around it. An interesting concept when you really think about it.

Preferably in silence.

"Fools, " said I, "You do not know
Silence, like a cancer, grows
Hear my words that I might teach you
Take my arms that I might reach you"
But my words, like silent raindrops fell
And echoed in the wells, of silence

7 Like • Comment • View 7 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.