Complex Numbers (Book)

Blog Calendar

◄ September ► 2018
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:

Turkey DrumStik

about 12 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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

September 18, 2018 at 1:16am

#941606

The Right Thing

I've been thinking about this story (warning: godsdamned autoplay video):

https://www.cbsnews.com/news/santa-barbara-california-teen-rhami-zeini-finds-pur...

A Santa Barbara, California, high school junior was driving home from school Wednesday when he noticed a black purse in the middle of the street. He rescued the purse from the roadway and was shocked by what he found inside: $10,000.

Okay, cool. Good on the guy. Did the right thing, etc. Also lucky the cops were honest. Could have easily been like "Ma'am, we found your purse. Oh, the money? We didn't see any money. Someone must have lifted it. What's that? Where'd we get the shiny new rims on the police cruisers? Um, DUI fines. Nothing to worry about."

Now, I'd like to think most of us would have done something similar. I don't know what the legal thing to do is; based on the founding legal principle of "finders keepers, losers weepers," it may very well be legal to keep the wad. But what's legal isn't always right and vice versa.

Still, it got me thinking about thresholds. Let's say for the sake of argument that you're the type who would return the money. Pretty easy in this case, given that it was in a purse, and purses tend to also hold IDs. By the Ethical Principle of Least Resistance, you can feel good about your choice with very little effort. Okay.

Now, very likely you've found a penny on the street (assuming you're in a country like the US that still uses pennies). Most of us don't even expend the minor effort it would take to bend over and pick the thing up. Besides, it's probably covered in germs, right? The penny stays. (For the record, I pick up pennies. And shut up about the "heads good luck tails bad luck" or vice-versa or whatever; that's nonsense. Money is always good luck.)

But what if it's a nickel, a dime, a quarter? A dollar? A $20 bill? At what point do you stop saying "hey look, free money" and start looking for the owner? Hell, what are the chances you'd actually find the original owner? That's where ID comes in. What if it's a tiny wad of $1 bills clipped to an ID? Then do you return it? (I would - that might indicate it's a stripper.) At some point between "stack of 100 $100's with ID attached" and "stray penny," we say "fuck it," and the founding legal principle of "finders keepers, losers weepers" takes precedence.

Looking at it from the loser's perspective (something I'm eminently qualified to do), if I lost $10k, I'd be upset, but I wouldn't expect its return. It'd be nice, sure, but I'd consider it's on me for dropping $10K on the street. Not that I'd ever expect to be in a position to do so, but I have, in fact, held that much cash in my hand before. Briefly. It's not as bulky as you'd think. Thinner than most paperbacks. Even thinner than my NaNoWriMo manuscripts, and worth a hell of a lot more.

It's not a simple algorithm, either, not for an individual. Suppose you're in dire straits, just lost a job, buried in debt. Would you still do "the right thing?" About to be evicted or foreclosed upon? In which case "the right thing" starts to get a little murkier. What if you're simply in a bad mood, or - well, if I found that kind of cash lying around and the accompanying ID said "Richard Spencer," I'd probably keep it - though I expect I'd donate it to something left-wing just to piss off that Nazi ass. Except he'd never know about it, which might mute my satisfaction a bit.

Anyway, just got me thinking about it. It's a hypothetical, like the trolley problem - not something you'd expect to encounter in day-to-day life. I will, however, continue to pick up pennies off the street. By the time I die, that'll make my estate about $1.23 richer.

4 Like • Comment • View 5 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.