Complex Numbers (Book)

Blog Calendar

◄ July ► 2022
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 6 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 8 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.

July 5, 2022 at 12:02am

#1034711

That's Hollywood

Hopefully we're all aware that movies are fiction. Even the ones based on real events are fiction. Still, they can give us the wrong idea, like how in Being John Malkovich they were able to get from Jersey City to Midtown in 15 minutes. (That was, incidentally, the most unbelievable part of that movie.)

4 Myths About Natural Disasters Movies Want Us To Believe

I'm not sure I'd go quite so far as to say they want us to believe it, Cracked. More like, they want to provide a cool spectacle, realism be damned.

But, just like movies have put it in peoples' heads that the asteroid belt is dense enough to provide an obstacle course for a spaceship (it's not), we've all gotten the wrong idea from watching big-budget movies. Yes, even me.

Anyway, here are some examples of how Hollywood egregiously uses our fear of apocalyptic events to bypass real and accurate science. It’s just that easy, we guess.

Look, I get it. Science is hard, and usually visually boring (except around stars and black holes, which, by the way, Nolan got the time dilation thing wrong there), so you want to go with what grabs a viewer's eyeballs. Even the ones that purport to get the science right (The Martian and Gravity, e.g.) don't. But I'm not linking this article to rag on the movies.

It's even possible to go too far with the "realism" critique. I think it was Neil deGrasse Tyson who pointed out that, in Titanic, the stars were all wrong for that latitude and time of year. I wouldn't know, because I've never seen the movie out of fear of having to listen to Celine Dion. I mean, if the stars were actually essential to the plot, sure. I can get, for instance, noting that the door (or whatever) that the chick was floating on at the end was actually wide enough for both of them. That's plot-related. Again, never seen it, just going by spoilers (the ship sinks, by the way).

Anyway. I'm just pulling those examples off my brain. Presumably, the author here did actual research. But it's Cracked, so you never know.

4. No, Ocean Impacts And Tsunamis Won’t Go Down Like In The Movies

I gotta admit that, after seeing fictionalized tsunamis as a kid, when I saw an actual one (on video of course), it was decidedly underwhelming. I mean, scary, sure, and I don't want to minimize the absolute horror that the victims went through, but it wasn't nearly as apocalyptic-looking as I'd been led to believe.

My sense of betrayal there is largely because I read Lucifer's Hammer, by Niven and Pournelle, as a kid. It was a meteor impact disaster novel before that kind of thing went mainstream. A hipster meteor impact disaster novel. I've forgotten much of the plot other than "meteor slams into ocean, shit floods, people die," but one scene will always be burned into my mind: an entire chapter devoted to a dude catching the giant wave resulting from the impact and riding it on a surfboard.

Great scene. Well-written. Exciting. Disappointing that such great SF writers as Niven and Pournelle could have gotten that science so wrong. In their defense, though, science advances and perhaps that was the best estimate of what would happen, at the time.

Galen Gisler, a senior researcher in physics and geology at Los Alamos National Laboratory... said that “the folklore has been that tsunamis from impactors will be the danger … The splash wave can be very dangerous, out to tens of kilometers, but beyond that, they fall away more sharply.” Gisler calculated that only a tenth of 1% of an impact’s kinetic energy will be spent on forming waves.

Spoilsport.

3. Dormant Volcanoes Don’t Simply Kick Back To Life Like In The Movies

I mean, I'd suggest just reading this one. It's not even so much about dormant volcanoes, but volcano scenes in general. I can excuse the one where Anakin Skywalker gets turned into Darth Vader because that's a fantasy movie set on another world, or the one where Spock nearly gets fried except Kirk tore up the Prime Directive, because that followed the Rule of Cool. But again, let's not pretend that these in any way reflect Earthly reality.

Still, when I was standing on top of Haleakala, I have to admit I was a little bit like, "What if this thing starts up again?"

2. You Can’t See ‘The Eye Of The Storm’ Inside A Tornado

I would have thought this one was obvious. Look at a tornado from the side. What's it shaped like? Usually it's all twisty. Thus, if you're lucky enough to survive the wind wall and you look up, you won't be able to see through to the sky above. I suppose maybe the really strong ones are more upright cylinder-shaped, but good luck making it through one of those.

1. Earthquakes Don’t Open Up The Earth To Swallow People Hole

Typo or pun? You decide.

Anyway, maybe not, but again... it looks good on screen.

So in conclusion, like I said, movies are fiction and we shouldn't be fooled that they reflect reality. And yet, I can enjoy them anyway, even though I know that the square-cube law would prevent anything like Godzilla from actually existing. Hell, part of my enjoyment is noticing where they get it wrong.

9 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.