Complex Numbers (Book)

Blog Calendar

◄ November ► 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:

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

November 6, 2020 at 12:03am

#997752

Gridlocked

I suspect I'm going to be an outlier here.

PROMPT November 6th

Would you ever take a trip to a place "off the grid?" Where would you go?

Short answer: No.

Long answer: HELL no.

Even longer answer with philosophy and life experience thrown in:

First of all, let's work out some underlying assumptions. I've driven through the stark deserts of Nevada and the sequestered mountains of Colorado, Washington State, and West Virginia. With Nevada in particular, it's possible to drive for hours without encountering civilization at all, or even mobile phone service. So I'm assuming, here, that by "trip" we mean something longer than a few hours, or even overnight. Also, by "off the grid," my mind jumps to those polar opposites: hippies and libertarians, each seeking a reprieve from what we call civilization for their own disparate purposes; there might be electricity, self-generated, or perhaps something even more primitive: survival in a pre-technological mode.

It's as if you've built yourself a mansion, and when you look at it, you decide, "nah, I'mma go live in a mud hut."

Fuck that.

I mean, hey, you do you. Obviously no one reading this is "off the grid" in any meaningful way, because to do so you had to access the internet, but I'm sure you've heard of the type of person I'm talking about: an acolyte of Thoreau, perhaps, or of some Eastern guru. It's not my intention, though, to disparage their way of life, or to insult the Amish, or rag on the Inuit; only to say that such a lifestyle is absolutely not for me.

But we're not talking about spending one's life cut off from the rest of the world, here; just "taking a trip." Even there, I have my limits.

I'm only alive right now because of technology. If not for medical science in particular, I'd be dead at least thrice over: once from complications of bronchitis when I was sixteen years old (resolved with a course of antibiotics), once from some weird infection of the optic nerve whose name escapes me right now but could have spread to my brain (again, antibiotics), and once from a heart attack (angioplasty and stents). At the same time, I'm perfectly aware that technology has its dark side: pollution, microplastics, toxic waste dumps, auto accidents, Justin Bieber. Still, on balance, I've already lived longer than I would have in a pre-technological era. I'll take that trade-off.

Now, again, don't get me wrong; I understand full well that some people feel the need to escape civilization for a time, going camping or whatever. I understand, yes, but it's not for me. I could probably spend one night without my CPAP machine, for example (and, last night, I was forced to do so because my nose was doing its Snotagara Falls impression), but after one night without it, I'm boned. But even absent that technological marvel, I've never enjoyed nor sought out camping for the sake of camping. I mean, sure, I did it some when I was younger, but I can't say I ever enjoyed it; I always wanted to get back to electric lights and books and my computer (this was even before the internet was a thing) and, primarily, heated rooms and showers.

Hell. I spent a shitload of money on a whole-house generator because I can't be arsed to go without electricity for extended periods of time, and we get power outages here. I excuse it by saying I need it for my CPAP and a foundation drain sump pump (it occurred to me one day that power outages usually coincide with the times when I desperately need the foundation drain to work), but it also keeps my internet connection on.

And now? Now I have personal goals that require me being connected to the internet on a daily basis. This blog, for one. I have written in it every day so far this year; in eight more weeks, absent a serious illness and/or the coming collapse of Western society, I will have written a blog entry every single day. Though... it's worth noting that, had this year gone as originally planned, there would have been gaps -- a trip to Europe and a trip to a dude ranch in Colorado; in both cases, I still wouldn't have been "off the grid," but I probably couldn't have been arsed to worry about blogging.

For another, I've got a good streak going on Duolingo -- 435 days as of yesterday. For those unfamiliar with the platform, that means I've done language lessons every day for well over a year. Now, a streak isn't really all that important; what's important is that I keep learning the language, but I'm obsessive enough to want to keep the streak going as long as possible. Doing lessons daily helps me learn and retain more of the language than if I only did it sporadically.

And yes, the internet can be poisonous. I think I avoid the worst of it, like Twitbook. But I have a thirst for knowledge and learning, and an insatiable curiosity, and the greatest marvel the world has ever created is the ability for us to learn about pretty much whatever I want, whenever I want. YouTube videos on quantum mechanics. Treatises on ethics. Where we stand on figuring out our universe. Chemistry, biology, physics, mathematics, cosmology, music, astronomy, psychology, history, philosophy, comedy, geology, art, literature... sure, sometimes I have to weed out the falsehoods and be critical about things, but like any skill, one gets better at it over time (at least I hope so). I trust that my blog entries when I'm not doing the 30DBC reflect this curiosity.

I wouldn't trade all that for time in the wilderness, not even for a single week. Okay, maybe for a day or two, because that too would satisfy my curiosity, but that's my limit.

All of this, of course, means that I will be utterly useless in our impending civil war and subsequent breakdown of society. I have only rudimentary survival skills outside of a technological milieu. I'm okay with that; like I said, I've been living on borrowed time since I was 16 years old. There are worse things than dying, in my view, and being stuck without technology is one of them.

So enjoy your camping trip or your sojourn in Antarctica or visit to Siberia or whatever. No, really, if that's your thing, go for it; I look forward to reading about it and seeing the pictures and/or videos (as long as the videos aren't vertical) on the internet. I'll watch the mansion for you while you're away.

13 Like • Comment • View 11 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.