Complex Numbers (Book)

Blog Calendar

◄ March ► 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	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:

Write_Mikey_Write!

about 17 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 18 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.

March 31, 2020 at 12:14am

#979755

Vive la Révolution!

Wrapping up entries for

Journalistic Intentions

[18+]
This is for the journal keeping types that come to PLAY! New round starts July 1!
by Turkey DrumStik

Why the hell is this a video?

Let me get this out of the way. This video is over 20 minutes long and it's just a computer geek talking the whole time. Yes, he's good at talking. No vocal tics, few pauses, knows his material. Good for him. But I just wasted 20 minutes watching a video when I could have skimmed a written article and gotten the same outcome.

There are reasons to do video. This is not one of them. Its only saving grace is that it's not formatted vertically like savages do.

Techie Talk

I'm not an idiot, and I've been using computers since the late 70s. But I'm not in the business. I have no idea what half the shit he was saying was. Something about processor speeds and CPU architecture, none of which was really relevant to the point he's making. While it does serve to establish his geek smarts, I think I got the idea after the first phrase of tech jargon.

Rotten Apples

He opens with an analogy with totalitarian Soviet Russia, comparing the Apple user experience to that sort of propaganda cult. I find this especially amusing, because one reason Apple went mainstream was a S*per B*wl ad back in 1984 (long ago when I actually watched football), giving them an opportunity to draw parallels with Orwell. In it, a freedom fighter (supposed to represent Apple) destroys a propaganda film from the Establishment (supposed to represent IBM at the time).

I mean, really, that one ad is probably what started the S*per B*wl ad fad, as well as launching Apple into the consumer spotlight.

Here it is: https://www.youtube.com/watch?v=2zfqw8nhUwA

The text at the end of the ad: On January 24th, Apple Computer will introduce Macintosh. And you'll see why 1984 won't be like "1984."

So yeah, irony.

Same As The Old Boss

The problem with revolutions is, and has always been, that all they do is replace one kind of power structure with another. The replacement power structure might appeal to more people, but I guarantee you there were those who mourned the loss of the French aristocracy during the Revolution. At least briefly, until their heads were separated from their bodies.

I've known a lot of Apple fans, even from before 1984. Some of them are, as the author of the first video above noted, cult-like in their obsession. I understand, to an extent -- their products have always been more elegant, both inside and out. I never owned one of their computers, though, because it's always been easier for me to game on the Windows boxes. But I used them for years; my first career boss was an Apple fanatic. But those machines couldn't run AutoCAD worth a damn, either.

Point is, for me it's a matter of picking the right tool for the job. When I wanted a music device, I picked an iPod, not a Zune. I still use it; I don't trust streaming to not take my music away from me.

And I don't listen to Apple fanboys trying to shame me for using a PC. For fuck's sake, it's just another company.

Just Another Company?

Well, okay, it's pretty much the archetypal company. Their propaganda machine works better than their actual machines, as our intrepid geek above pointed out. This gives them staying power, despite the efforts of their detractors.

I like to point out that Steve Jobs started a company, with a couple of other guys of course, in his garage, and at the time he died, it had grown to be the most valuable publicly traded company in the world by market capitalization, surpassing not only Microsoft but such venerable giants as ExxonMobil and GE.

They're not that, at the moment, but that doesn't matter; the point is that now the revolution is long over and Apple is the Establishment.

2 Like • Comment • View 2 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.